Ed is right about volume, all things being equal. 10X power gives you 10db volume increase, which is about double.
Keifer brings up a good point, that many low power amps often don't have the more sophisticated gain stages bigger amps do. Very often they don't have as many options in terms of channels, fx loops, etc.
Also, a small amp may not be able get clean sounds at it's limit, where a larger amp will be able to crank out plenty of clean sound at the same volume.
Something that doesn't get brought up much in the big vs. small debate- a 100W guitar amp can be twice as loud as a 10W amp. But the key is that if both amps are set the same, the 100W will be twice as loud across the whole dynamic range of the guitar.
What I mean is this:
Amps put out watts in proportion to the input signal. In this case it's the signal from the guitar. If you plug into both amps, the 10W puts out 10W, the 100W puts out 100W. Now turn both amps down to 50% output. The 10W now puts out 5W, the 100W puts out 50W. Still twice as loud. The same thing happens when you turn the guitar volume down.
The point is that unless the 100W amp is set to put out 10W, it will ALWAYS be louder than the 10W amp, not just at the peaks. Strum the guitar quietly- the 100W will be louder. Turn on the distortion and chug away- the 100W will be louder.
Rant-
For practice (and gigs) it's amazing how much louder your amp will be to you if you actually point it at your ears by tilting it or getting it up off the ground or both.
Many guitar players seem to think that their ears are either behind their knees, in their asses, or in a completely different part of the room. They will play with their amps on the floor behind them, next to the drum kit, or on the other side of it, or pointing at the bass player. And wonder why they can't hear it.
Your ears are in your head. Best results will come from pointing amp at ears, or ears at amp.
If you don't want your amp pointed at your ears because it's too loud, chances are nobody else wants it pointed at them either.
Rant off.