Nowt to do with wattage. All abart the efficiency of your speakers. A 20w amp driving an efficient pair of speakers will sound better than a 30w struggling to move the drivers in something less efficient. Measurements usually given in the hifi mags - anything above 87 is reasonably efficient, 86 and below and you'll need summat with a bit more grunt to make them sing. People constantly worry about "blowing" speakers by using too powerful an amp - the reality is that more damage is done using a low-powered amp with inefficient speakers
Be careful with descriptions...look for watts in RMS (Root mean Square) rather than PMPO (peak music power output) The latter can make a system sound more powerful than it is as it measures those transient peaks you get in music whereas RMS is the 'average' sustained level and therefpore a better guide to the capability of your system. Mickey Finn has it spot on. A low powered amp driven hard 'clips' on the transient peaks which causes a 'voltage spike' usually at high frequencies. Think of it like suddenly putting 80 volts through a 10w bulb like those old camera flash bulbs... Now do the same to your H.F speaker coils. Get the picture??