By and large, yes. But you'll find guys right here on this forum running amps that produce less than ten watts, and that cost several thousand dollars. So there is an issue of quality too.But really, an amp is nothing more than a signal multiplier. That's its job - Nothing more and nothing less. You'll find that the places where amps are really set apart from one another these days is in their power levels, clipping resistance, signal to noise ratios and (in the case of class AB amps) their ability to pass through the zero crossing threshold without distortion. Internal power supplies are a big deal here - as much so as the signal amplifier components - so more expensive units will perform better as they approach clipping. All these things translate pretty well in the two figures of signal to noise ratio and of total harmonic distortion, but since they are often measured at moderate power levels where it is only a fraction of a percent, they can really lose their meaning. Certainly, you're not going to measure performance when the amp is nearly clipping, and that's what we're really talking about here.
Still, the bottom line is that two amps should sound pretty much the same at a watt or ten, and if so, then they're doing their job. If you've got an amp that sounds very much different at these levels, it is my opinion you should throw it away because, again, we want the amp to act only as a multiplier and that's all. It should add nothing and take nothing away - Just multiply what's there precisely and faithfully.