I played with my clan to 50 and then went through it again. There was about 8 of us and we had two of every class and these were the conclusions:
Even going full SMG spec using the best smg's that 5 players could find, my group all agreed they sucked and I ended up playing with every single type of weapon besides smg's with Lillith. And with rockets, even with 100% accuracy/hit rate the rockets are just not worth specing in and rarely worth using. We only found one that was worthwhile to use for a few levels and it was quickly obsoleted. One we later found at level 20 that seemed to be a pretty good electricity based one was also fairly worthless because most of the enemies we fought that were electricity based were the flying ones which made hitting them difficult.
Even using the item editor to make the best possible SMG and rocket launcher we could think of still gave a lackluster result. Rockets don't have enough AoE to make them worth their slow travel speed and low ammo. They should really up the damage on these immensely and try to make them a weapon you use on occasion to kill really hard stuff instead of trying to balance it as a weapon that Brick can use as his primary weapon.
SMG's just don't have the punch or the range/accuracy to justify such low ammo.
As for the classes, which one is the most fun to play is up to debate. Which one is the best...not so much.
It depends on if you are doing multiplayer a lot, but let me explain each in detail here.
Lilith is by far the most overpowered, mainly due to her special ability.
Use in Multiplayer-Yes. One or two Lilths running around completing travel quests and talking to people saves the party hours of time while the others power through enemies. Everyone gains exp regardless of distance.
The ability to become invincible and be able to travel super fast is enough, even without it doing damage on start and finish, which it does.
With phase walk you will:
-Never die or get trapped
-Save hours of walking places (can do travel quests with ease)
-Level Faster
-Be able to farm dungeons obscenely fast. I can run through and hit all the chests in the crystal caves in less than two minutes with Lilith at any level, and with anyone else it would take me 5x as long (or be impossible at lower levels). This is made even better because Lilith can use a catalyst class mod that increases the chance to find rare items (only mordecai can also do this).
Her only downside is that some of her abilities/class mods focus on SMG's which are by far the worst weapon type in the game. Going through to 50 I was using everything EXCEPT smg's with her. Even when I found one that was OK I'd only use it when I was out of ammo with ALL other guns, and even then the SMG ate through the maximum ammo amount way too fast. SMG tries to be a little of everything and fails terribly because of it.
Brick
Use in Multiplayer-No. His special ability is actually a hindrance to the team. Running around right next to a monster spamming large effects only means that your teammates will be unable to get critical hits as they struggle to not target you or the spam you create. The speciality with rockets also spams effects way too much. In multiplayer, monsters may become so powerful that meleeing them with your special can result in near instant death.
Pros
-High life means you personally shouldn't be dying too much and some of your class mods can give that benefit to your team in multiplayer.
-Special is useful in singleplayer and quite funny.
Cons
-Above mentioned multiplayer hindrance and weaknesses.
-Rocket Launchers are underpowered and underammoed even with rocket ammo regen.
Soldier
Use in Multiplayer-Yes.The turret can be very helpful to the team as can the class mods. It is even viable playing with 4 soldiers (although I'd take at least one Lillth).
Pros
-Turret is very useful, though less in singleplayer.
-Both assault rifles and shotguns are good weapon classes.
-Can easily switch skill selection from a singleplayer build to a multiplayer one.
Cons
-Lowest potential for damage output by himself.
Mordecai
Use in Multiplayer-Probably not. The more people are playing, the harder it is to get criticals as their attacks and movements can often get in the way and make precise aiming harder. Even the birds positive effects such as extra ammo and items are not needed when you already have soldiers.
Pros
-Criticals and damage output are amazing.
Cons
-The bird is pretty much shit at all levels (especially early on).
-Pistols, which often have scopes, often serve the exact same purpose as sniper rifles so the specialities in both is kind of redundant and not as useful as something like assault rifle/shotgun combo.