That would greatly depend on parts, some of a manufaturers higher power amps also emply better parts so it is hard to make a general claim that would always hold true. But as far as you asked with same general construction a higher power amp would more easily drive speakers, but not pushing any real watts it is most likely gonna sound good regardless.
Power and Sound Quality, Other Things Being Equal
Suppose that a manufacturer has several amps with the same basic construction but with different amounts of power (e.g. NAD C320BEE, C352, C372). Will the highest power amp sound better than the others at moderate volumes or only when you crank up the volume?