A higher power sub would create clipping of the amp when you drive it hard.
Oh and Retepetsir if I'm so wrong correct me instead of just sayin I'm wrong.
It's not the sub that would create clipping, it's the amp that would be driven into distortion and clipping when you push it too hard and it can't provide good clean voltage any longer, speakers don't like square-style waves, they like nicely rounded tops/bottoms! Driving the amp too hard for long enough can either overheat and kill the sub voice coils or kill the amp, or both.
You can run a subwoofer with a higher rms rating than the amp thats driving it fine, you just need to set the gains properly so that the amp isnt driven to produce a dirty signal at any point. You can also quite easily run a lower power sub off of a higher power amp (as you say), quite a bit higher actually, again as long as you are careful in setting the gains. This way is best (overpowering) as you then have headroom in terms of the amps power, often producing music with better dynamics, etc.
My sub is rated at 300wrms but is quite happily being fed nearly 1kwrms without any problems.
You actually want a higher RMS amp than sub, not the other way around. Ignore the peak power/max power/pmpo ratings as they mean naff all.
Something like a 300-400wrms amp (at 4ohms for example) would be fine on a 200-300wrms 4ohm subwoofer if setup correctly.
Bass in a car should not be rough and distorted! Build your own box, build a ported box and tune it to the bass extension that you want along with the size of enclosure, etc (try WinISD via Google, its free). If you are a bit more adventurous try an infinite baffle setup (IB), passive radiator or similar. Experiment, make it sounds better, just have fun
No headunit reaches even 4x45w. Again that's peak power. Actual rms is nearer to 15-20wrms....hardly earth shattering.
The big manufacturers (well, decent ones) still quote rms figures, you just have to look for them in the specs (Alpine, Pioneer, US Amps, Vibe, Genesis, DLS etc all do).
