How Much Difference Does a More Powerful Amp Make?

Easy, just think the differences in horse power in a car, as you are climbing Pike's Peak.

For inefficient speakers with low impedance drops a more powerful amp can make a dramatic difference. For your average speaker you may perceive better or tighter bass and more "ease" at louder volumes. But then again you may perceive nothing different at normal listening levels and sometimes lower powered amps do indeed have better sound than their big brothers.

Amp rated at lower continuous power might have higher momentary power. Average power needed for music is only few percent of peak power unless you listen to sinewaves.

Power specifications give only general guidance but all depends on particular amp design. Chances are, when comparing amps from the same line/company, that higher rated amp will be louder but 15.7% difference in loudness might not be worth extra money.

Comparing to a car is a little misleading since 10x power is only 2x louder (exponential scale).

The point has already been made but here it is in a cute form.
If the first watt sounds bad why would you want several hundred more of them?
Quality is the key and the usual recognition that some speakers really do need high current amplification to sound best. Essentially I am just agreeing with most of the comments thus far.

The W7 is the sweeter sounding of the two amps . I would never trade finesse for more power , and although the W8 may sound more powerful we are only talking about a 2dB difference .