I know this is a 2 month old thread, but it's still a relevant discussion.
My favorite is easily the Gunner. 5/5 Leg It + Short-ranged shotgun gives the Gunner the highest close range burst damage in the game. Once all 12 shells are unloaded, switch to MG and pop Hero Shield to mow down any residual health.
I play the other two classes and Gunner is the hardest to master. I have a level 15 Soldier and it's the most effortless to dominate with while Gunner can take a lot of strategy just to stay alive between fights.