Uses more stabilizers, gives a different feel because each arm is working on it's own. Good for variation as well. I personal like incline db much more than barbell, but flat barbell more than flat db.
I believe it strengthens your core because the lack of stability forces you to recruit more muscle fibers. Those synergist muscles really get zapped by just trying to keep the dumbells aligned.
If you are new to them, your chest might not be as strong as you thought and you will not be lifting as much as you do with the barbell.
Barbell bench presses work your chest more overall but dumbbell presses are better for your stabilizing muscles (I likethem for my triceps) and also don't require a spotter to lift to failure. Everyone's range of motion is different but dumbbell presses have the bigger potential. I would switch off every few weeks or so to add variation to your workout,really hitting your chest in different ways.
I'm a lot stronger than most people my size with dumbells but a little weaker with the bar. Dumbells i can get up to 80 six times, but with the bar, my last set is about 165. Why is that?