Assault : Assault is mainly used to kill as quickly as possible. It's strong firearms makes up for the lack of protection.
Medic : Medic is used because of it's healing qualities and it's fairly strong sub-weapon.
Sniper : Sniper will be used for it's long range abilities and strong bullets for close range.
Aug is the only sniper weapon that can be used as a sniper rifle and an assault weapon.
Engineer : Engineer is the only one that can not do as many things. The only special abilities are the land mine and the ammo boxes.
Heavy Trooper : Heavy trooper can instantly kill anyone up close if you are pointing at them, or where they are standing. They can also destroy vehicles.
Overall, They all have their own abilities. No one can say whether one is better than the other. It's how you use it.