As an example of what John is saying; I'm currently running a 10" sub with a 250W plate amp and it's barely adequate(it bottoms out way too soon)in my 16x28 room.

I found a dandy 12" driver that will electrically and physically fit my cabinet beautifully that has a better SPL and more travel and allow me to continue using my "small" 250W amp. So, yes, I'll be getting more output, with less input, with a larger more efficient driver.