An underpowered amp means you will drive the amp into clipping when pushing at louder volumes. When this happens, it's a bit like feeding a square wave through your speakers. This is extremely bad for the speakers (in fact worse than driving them over their rated power level) because a transducer does not naturally behave in that manner. Trying to "hold" the driver out at the clipped output to mimic the square waveform is a bit like feeding bursts of DC current through the voice coil. Of course, that just means you've now turned your voice coil into a heater, which as you can imagine is a very undesirable outcome.
So I repeat, it is better to be overpowered than underpowered. Now of course, you don't want to be driving past your rated speaker limits in the first place, but going over with a clean waveform is significantly better than clipping out underneath.