I'm analyzing the effectiveness of all classes in various roles:
Single-target Damage (PICK): The ability to deal damage to a single target, duh. Doom ailment is also included in this, but I usually skip over other DOTs.
AOE Damage (AOE): The ability to clear large amounts of mooks in a single turn.
Single-target Disruption (DIS): The ability to lock down a single enemy and prevent them from going out of control.
Crowd Control (CC): The ability to debuff large amounts of mooks at the same time.
Tanking (TANK): The ability to not die, mostly by resisting damage.
Self Sufficience (SELF): The ability to buff or heal oneself in various ways.
Support (SUPP): The ability to buff and heal the rest of the party in various ways.
AP Generation (APG): Probably the most important, the ability to use abilities. Don't let the name fool you, I take into account skill costs and AOE is heavily linked with it.
Champion
PICK (B): One of the few classes that starts with a high damage Weapon, plus Xross-Xtrike and Hero Sword Attack make for good single target damage.
AOE (A): Clean Sweep can clear 5 mooks even with +HP thanks to the Claymore 2 base damage.
DIS (A): Disabling Hit will lock down one dangerous enemy for a long time.
CC (D): Nothing beyond single target abilities.
TANK (A): Super high HP and second best starting Armor, nullifying normal mook attacks even with +Atk. Even better with Duck and Cover, and for an ally. Only for physical attacks though.
SELF (D): Nothing outside of Duck and Cover.
SUPP (C): Taking hits for allies (and no damage from physical attacks) is all.
APG (C): Nothing until Clean Sweep, which usually refunds itself.
Elementalist
PICK (B): Several skills deal single target damage, with special mention to Conflagration for the additional On Fire damage.
AOE (A): Ice Lances can clear 5 mooks even with +HP.
DIS (A): With a mere 2 AP the Elementalist can put a single enemy completely out of action for 4 turns. Thunderclap also inflicts a significant debuff.
CC (B): In case Ice Lances somehow doesn't kill, it will inflict Slow on up to 5 enemies.
TANK (D): Very low HP, Scale Armor does enough to protect against normal mooks, but the best protection is for rare damage types.
SELF (D): Nothing outside of Scale Armor.
SUPP (C): Fogcall is an excellent Evasion buff that usually will benefit allies more than enemies.
APG (C): Nothing until Ice Scales, which usually refunds itself.
Faerie
PICK (B): Only Faerie Fire inflicts a lot of damage, but it's a lot of damage.
AOE (F): Nothing whatsoever.
DIS (A): Several extremely strong single target debuffs for variety on shutting down an annoying enemy.
CC (D): Nothing beyond single target abilities.
TANK (D): Only regarding Magical damage, and on one of the lowest HP class.
SELF (C): A significant buff to Hit and Evasion that lasts for quite a while.
SUPP (B): Cheap heal that also removes some ailments.
APG (F): Nothing whatsoever.
Gorgon
PICK (C): Only ok with Eye Beams. Petrification is absolutely not worth 9 AP to kill a single enemy in 3 turns while giving them mixed bonuses.
AOE (F): Nothing whatsoever.
DIS (B): A couple cheap and long lasting debuffs good for setting up kills and preventing skill usage.
CC (D): Nothing beyond single target abilities.
TANK (D): No armor, and a small HP bonus.
SELF (C): Potentially great self healing with Regeneration.
SUPP (F): Nothing whatsoever.
APG (F): Nothing whatsoever.
GIFTA
PICK (D): Acid Spray will deal some damage over time, but nothing special unless stacked repeatedly.
AOE (F): Nothing whatsoever.
DIS (B): A couple cheap and long lasting debuffs good for setting up kills and preventing skill usage. Same as Gorgon.
CC (D): Nothing beyond single target abilities.
TANK (D): OK starting Armor, nothing more.
SELF (A): Extremely good Evasion buff and self healing.
SUPP (C): Pep Talk is an ok buff, but it's free.
APG (B): Not only are their abilities all cheap, they can generate free AP with Pep Talk.
Martial Artist
PICK (B): Painted Strike and Masterpiece deal massive damage for their cost. Requires setup though. Artistic Collab however doesn't.
AOE (B): High-Kick Paint Tornado can wipe 3 mooks easily. Dazzling Art Show can do immense damage to a lot of enemies with proper setup.
DIS (C): Joint Smack is a good disabler.
CC (C): If somehow enemies survive Dazzling Art Show they will all be inflicted with Blindness.
TANK (F): Nothing whatsoever.
SELF (C): A pretty good and free self boost.
SUPP (F): Nothing whatsoever.
APG (D): The AOE abilities are high cost and will at most only refund their own cost.
Masterchef
PICK (D): Only the basic attack.
AOE (F): Nothing whatsoever.
DIS (F): Nothing whatsoever.
CC (F): Nothing whatsoever.
TANK (D): Nothing beyond Mystery Stew.
SELF (B): Snack is ok and several abilities also after the Masterchef themselves.
SUPP (A): The absolute best, with several good buffs that affect the whole party, including Mystery Stew.
APG (A): Snack is more effective at generating AP than trying to kill mooks, making it a higher priority.
Necrolover
PICK (A): Between The Black Kiss, Saturday Night Fever, Total Eclipse of the Heart and the possibility of 6 extra allies attacking a single target, the Necrolover can decimate a single target in a wide variety of ways.
AOE (B): Depends on the raised mooks, but up to potential 7 different targets.
DIS (A): Heel Strike is a cheap attack for a good debuff. Saturday Night Fever will ruin a target.
CC (D): Nothing beyond single target abilities.
TANK (F): Nothing whatsoever.
SELF (C): Wound Salt can provide a good damage buff.
SUPP (C): Wound Salt can provide a good damage buff to allies as well.
APG (D): Nothing until Waise Fwom Your Gwave, after which it's largely up to chance.
Ninja-Samurai
PICK (A): Zanzetsuken can do massive damage and other skills also do large amounts of damage.
AOE (A): Several skills that, despite low damage, can affect either 3 or all enemies.
DIS (D): None of the debuffs do more than prime the targets for taking even more damage.
CC (B): Can apply debuffs to all enemies, priming them for a complete wipeout.
TANK (D): Not much beyond Evasion tanking.
SELF (B): Massive +4 Evasion buff that renders the Ninja-Samurai almost unhittable.
SUPP (D): At most, priming enemies.
APG (A): Starting with Kunai Trio, a cheap ability that can grant up to 3 AP, and after that the all enemy damaging abilities can self sustain almost indefinitely if it weren't for low initial AP cap.
Noble Blade-Star Crusader
PICK (A+): Literally the only thing they're good at, and depending ultimately on their Weapon. Combo can get ridiculous.
AOE (F): Nothing whatsoever.
DIS (C): They also do ok at this with Armbind and AP lowering.
CC (D): Nothing beyond single target abilities.
TANK (F): Nothing whatsoever.
SELF (F): Nothing whatsoever.
SUPP (F): Nothing whatsoever.
APG (F): At least the abilities other than Combo are cheap.
Numerologist
PICK (C): Good potential all around, but entirely dependant on RNG and Weapon, save for Rig the Slots.
AOE (F): Nothing whatsoever.
DIS (B): Enthropy Die can do a good number on an enemy.
CC (D): Nothing beyond single target abilities, despite Skew the Scales being random.
TANK (F): Nothing whatsoever.
SELF (D): Nothing unless Skew the Scales buffs them.
SUPP (C): Skew the Scales is a pretty good buff combined with a pretty good debuff.
APG (F): Nothing whatsoever.
Pilotmecha
PICK (B): Fully charged deals 15 damage to the main target and other abilities do good damage as well.
AOE (C): Positron Artillery Beam will do good work on 3 targets.
DIS (B): Don't underestimate Irradiated debuff.
CC (D): Nothing beyond single target ability.
TANK (B): Energy Barrier nullifies all incoming damage (up to 7) rather than reduce specific types of damage.
SELF (B): A great Evasion buff lasting for more than one turn makes it even better.
SUPP (F): Nothing whatsoever.
APG (C): Positron Artillery Beam is cheap and will at the very least refund its own cost.
Puppet Master
PICK (B): By proxy, with several high damage puppets, and directly with Great Sacrifice.
AOE (B): By proxy, since each puppet can attack different enemies.
DIS (D): Nothing specific.
CC (B): By proxy, with Magic Doll's Light Flash, since it affects all enemies.
TANK (B): Ok armor, can protect themselves and others with Guardian Dolls.
SELF (C): Can restore puppet HP by a significant amount but not their own.
SUPP (F): Nothing whatsoever.
APG (B): Each puppet will generate AP for the Master, and their own abilities don't have cost, making this one of the most efficient classes.
ROBO
PICK (B): Has decent damage on various skills, especially Micromissiles.
AOE (A): Great one on Devastator Laser.
DIS (C): Cryo-Beam does an ok work even if it doesn't freeze.
CC (D): Nothing beyond single target abilities.
TANK (C): Best starting Armor, nothing beyond that.
SELF (C): Very needed Self-Repair skill is also great.
SUPP (B): Technically Lock On only counts for a single enemy, but a resurrection is great to have.
APG (D): Nothing until Devastator Laser, which only does enough to sustain itself.
Sage
PICK (D): Nothing beyond attacks.
AOE (F): Nothing whatsoever.
DIS (F): Nothing whatsoever.
CC (F): Nothing whatsoever.
TANK (F): Nothing special, low HP and ok armor against magical.
SELF (F): Nothing else.
SUPP (A): Minor heals, resurrection, and a major damage buff against a single target.
APG (C): Bestiary Check provides free AP generation.
Skyranger
PICK (B): Ok damage on various abilities, especially High Noon with its (potentially suicidal) quad damage.
AOE (C): Shortbarrel does good work on high HP enemies.
DIS (C): Can inflict a few debuffs for a short time.
CC (D): Nothing beyond single target abilities.
TANK (D): Only Evasion on their starting Armor, which gets suppressed under High Noon.
SELF (F): Nothing whatsoever.
SUPP (F): Nothing whatsoever.
APG (F): Nothing until Shortbarrel, and even then it can't refund its own cost.
Sorceror
PICK (D): Nothing that stands out.
AOE (D): Good one on Chain Lighting.
DIS (F): Nothing whatsoever.
CC (F): Nothing whatsoever.
TANK (B): Bejewelled and Scale Cloak are both good defensive buffs that can be self applied, but very low HP.
SELF (D): Sorceror can also summon a Ghost Dagger for themselves.
SUPP (A): Great and varied buffs, including the powerful Quickening.
APG (D): Chain Lighting can generate AP as long as RNG determines good hits.
Uwu-child
PICK (D): Nothing special.
AOE (F): Nothing whatsoever.
DIS (F): Nothing whatsoever.
CC (F): Nothing whatsoever.
TANK (B): Good starting Armor, good Armor buff on Blobknight.
SELF (A): Self heal, self clear, self buff for fighting.
SUPP (A): AP and HP restoring, potentially on all allies, good buff and a powerful resurrect.
APG (F): Nothing whatsoever until they learn to self-stack.
Ültramarine
PICK (C): Good single target damage on some AOE skills.
AOE (A): Great skills for various occasions, including a high damage all target.
DIS (D): Nothing beyond AOE.
CC (B): Do not underestimate Irradiated, especially on everyone left alive.
TANK (D): Good starting Armor, nothing else.
SELF (C): Great self damage boost, but reduces their HP.
SUPP (F): Nothing whatsoever.
APG (B): After a mere one kill, Blunderbuss can generate a lot of AP.
Wizzard
PICK (C): Nothing special beyond a setup Chain Lighting.
AOE (D): Good one on Chain Lighting.
DIS (D): Nothing beyond AOE.
CC (A): Light Flash might be the best CC ability.
TANK (B): Despite having the lowest HP, Stone Skin and Arcane Shield can make for a surprisingly resilient Wizzard.
SELF (D): Afterimage is just barely ok since it only lasts for one attack.
SUPP (B): Can boost the tankiness of anyone significantly.
APG (A): Energize is another AP generation that's plain better than attacking, but Chain Lighting has the rare potential of 1 more.
Zubatman
PICK (C): Can do good against armored enemies, but nothing beyond ganging up.
AOE (D): Only if summons remain to attack other enemies.
DIS (B): Forgetfulness is ok to have.
CC (D): Nothing beyond single target abilities.
TANK (D): Ok armor, terrible HP.
SELF (C): Can regenerate one HP with Life Drain and boost Evasion for 2 turns.
SUPP (F): Nothing whatsoever.
APG (F): Nothing until summoning more allies, which costs a significant amount and flee very easily.
Champion (21/A): Great physical tank, great AOE and disruption, great frontliner all around.
Ninja-Samurai (21/A): Really good at dealing with enemies in general, plus a Smoke Bomb to help not die.
Elementalist (20/B+): Also great AOE and disruption, but not much in the way of other stuff. Great damage variety.
Wizzard (19/B+): Great AOE debuff, good tanking self buffs, AP generation. Less AOE kill than Elementalist.
Puppet Master (18/B): Really complex class, extremely versatile, needs time and weapons to set up to full potential.
ROBO (18/B): Good start and good abilites all around for various roles. Nice AOE.
Pilotmecha (17/B-): Good attacks and ways to avoid taking damage.
Ültramarine (16/B-): Greatest AOE coupled with damage buffs to disable and potentially wipe even several named units at once. Otherwise nothing much.
Necrolover (16/C+): Great single target abilities, but will take a long while to build up since raised mooks don't restore AP.
GIFTA (15/C+): Generally superior version of Gorgon, good all around but nothing of note.
Faerie (14/C+): Great disruption, good support and self buff, ok single target damage, awful survivability.
Martial Artist (13/C): Great potential that needs a lot of setup to work.
Masterchef (13/C): Super specialized at supporting but party wide healing and damage boosts are great.
Uwu-child (12/C): AP and HP heal is great, especially for all party. Otherwise only self serving.
Sorceror (11/C): Absolutely great buffs, unfortunately no heals.
Zubatman (10/D): Awful class all around like Gorgon.
Numerologist (9/D): Jack of all roles, doesn't do anything that well.
Gorgon (9/D): Mostly atrocious and generally not worth the few disruption and extremely long winded petrification.
Skyranger (9/D): Like Numerologist, does a lot of things but nothing too well.
Noble Blade-Star Crusader (8/D): Crippling overspecialization at it's best, only works with single targets, but can get ridiculous over time.
Sage (7/D): Even more crippling overspecialization, low AP cap, does what Masterchef usually does but worse. Potential for great boss killer combination with multihit classes.