My actual sub as you can see in my signature is a Pyle 10" very old passive sub, I have no idea of the specifications, powered by a vintage Nec integrated amplifier (75w/ch/rms) in mono mode.
The Klipsch RW-10 is powered by a 260 watts continouos amp and it goes down to 25HZ.
Unless you have really bad room acoustics (generally from a strangely shaped room, or very poorly damped) I wouldn't worry too much. All things being equal, you will hear an improvement in bass/sound quality going to a better subwoofer.
Seeing the increase in power you are talking about should get you louder bass potentially, but the quality of sound will be based on proper set-up (calibration), placement, and room effect, and the other stuff I said in the earlier post. Many people experience gains or nulls of certain frequncies due to the size/shape of the room, so yes, that too will have an effect.
Many people tend to try and set up their sub by ear, and that almost always ends up causing the sub to run louder than if it were properly calibrated (using a good test disc and SPL meter).
As I said too, I noticed a dramatic improvement in overal SQ with my Ultra. Proper bass levels will also affect the mid and treble frequncies of your system. For me the overall effect was a very pleasing improvement.