How Much Difference Does a More Powerful Amp Make?

IMHO, and perhaps more so with ss amps, having some extra power beyond actual use, is worthwhile in that it can keep an amp from stressing near it's clipping point.

The first Watt of a more powerful amplifier need not be worse than the first Watt of a less powerful amplifier. Furthermore, a more powerful amplifier can often provide better power longer than a lower powered amplifier, even though it hasn't exceeded the total power output of the lower powered amplifier.

If one listens to music at levels that come near the levels one might hear at a live venue, and that includes unamplified concerts, under powered amps can be subject to clipping during peaks. Fairly high powered SS amps without global feed back have been available since at least the 1980's. Some ss Class AB amps lines are able to stay closer to a Class A bias longer, as their total power output levels increase.
http://myhometheater.homestead.com/splcalculator.html
http://www.stereophile.com/content/threshold-stasis-sa12e-power-amplifier-page-2

Larryi, I think in a typical setting, a single 86 dB/W efficient speaker playing at one meter in free field (no room)with only 20 Watts available, might be significantly less loud than 99 dB.

http://myhometheater.homestead.com/splcalculator.html

I would guess that very few actually listen in such a manner. In what I (admitedly arbitrarily) suspect might be a more typical setting, using two speakers that are 86 dB/W, placed within 2'-4' from a roomer boundary, and heard from a distance of 3 meters would require closer to 45 Watts to achieve 99 dB

Though often cited, I don't believe the reason one typically doesn't listen at average levels of 99 dB because (the speakers) "...would be compressing like mad from overheating.", but, though appropriate for musical peaks, 99 dB is just uncomfortably loud for sustained listening.