I'm tired of hearing that LA is a viable or equivalently powerful AI class due to its mobility. As much as I want it to be true, and I've played LA a LOT, it simply isn't. Maybe in any other game that jetpack would be a big deal, but the nature of planetside 2 works against the LA.
A) Any battle that's more than 48 v 48 you can expect to have extreme difficulty jetpacking anywhere useful, period. There's so many players that every conceivable route towards any of the capture points is going to be observed and guarded. I only ever pull LA on tower bases and biolabs for the reason below.
B) Level design. There is no cover on the tops of buildings. Most bases have very little if any verticality. Large battles always devolve into progression through chokepoints, making mobility pointless, and to no-one's surprise HA is best at dealing with chokepoints (it used to be MAX-units but HA counters MAX so hard that the MAX-rush tactic has fallen out of use completely). Even in bases that provide alternate routes around chokepoints, the battlefield is simply so crowded that any and every path is a guarded chokepoint at all times.
C) You don't get to carry piles of medkits like the HA because you're carrying C4, and since you're flying around you'll never be near medics. As an LA carrying C4 is practically mandatory, it's your only counter to MAX units and vehicles. HA on the other hand, can rocket vehicles, and rocket + anti-MAX grenade enemy MAX units, in addition to being able to instantly heal himself to full health four times. (also, we should petition for DBgames to rename the anti-vehicle grenade to anti-MAX grenade :3)
SMGs absolutely murder LMGs at close range. They have 900 rpm.
D) SMGs have a quicker time-to-kill over LMGs, but not enough to negate a heavy shield that just up and gives them +60% health. Carbines on the other hand are strictly inferior to LMGs.
Additionally they are used by infiltrators and LA's that should get a drop on a HA.
E) Fantasy scenario (see A & B above, F below). Even in the situation that you successfully get the drop on an HA and kill him, shield or no shield, you will be murdered in short order by the other ten players standing around, the battlefield is too crowded for "get the drop on" to be a viable argument in anything but small fights. Don't even get me started on how small fights are dominated by 'mlg' outfits, further forcing the average joe player into big brawls lest he be absolutely useless against these absurdly skilled players.
F) You will never have the element of suprise (as LA) if there are any motion sensors around, ever, and for some reason the HA can use the crossbow with its sensor dart, further alienating "get the drop on" from the reality of planetside 2. If you play on emerald and have ever went to a fight against vanu you know just how bad the sensor dart spam gets.
The arguments in favor of LA/infil are the same ones that would make sense if this were a 12 v 12 team deathmatch game, and they would certainly apply if the mobility classes had room to breathe. But this is planetside 2, where mobility is the equivalent of being a TF2 scout and every pathway has an engineer turret on it.
I have 1000+ hours in this game, over 15% of that is LA. I absolutely love the light assault class, but I refuse to use LA if it's not a tower/biolab.
TL;DR - mobility is not an argument in favor of the LA class because battles are so crowded with players that the mobility is rendered moot.
And regarding the HA, basically everything @kanil said.