Have you played Borderlands? You've pretty much described it to a T haha.
Far Cry for sure
Just Cause 2 is RIDICULOUSLY fun and dirt cheap too.
Saints Row 3 was surprisingly not bad, a really silly takeoff of the GTA formula. Also really cheap because of THQ going out.
If you hadn't mentioned powers, I'd say Deus Ex, yea it's stealthy, but you can play it as a straight up shooter if you want to as well. For the boss fights it actually works out better if you do.
Have you tried Infamous? Not technically a shooter but pretty close. If you're a PSN Plus subscriber the 2nd game's free.
Spec Ops: The Line was pretty good, if you can get it cheap. The storyline is one of the better ones in recent military shooters imo.