Want to use a carbine, be mobile and use more grenades?
Go Vanguard, Assault Spec tree. Not the strongest DPS variant but gets the job done.
Also, BH is a mirror class to the Trooper (as some already mentioned), it's smoother and more fluent on it's attacks but Trooper balanced that out with the ammo vs steam thing. Mainly because steam on BH builds up VERY fast and doesn't stabilize as fast as the amount of ammo you can still have on the gun. Although that SERIOUSLY depends on how people manage their character.