According to my basic electronics book, MOSFETs are more "rugged and reliable" than bipolar transistors, and can make for a "simpler, more temperature stable" circuit. Hence their popularity for car audio, I suppose.
The Aczel and Rich paper that mtrycrafts cites (I am familiar with the simplified version that appeared in The Audio Critic) says that it is harder to make a really low distortion MOSFET amp, for various technical reasons that frankly I do not understand. Also according to Aczel and Rich, the often made claim that they sound like tubes because they allegedly operate on some of the same electrical principles is an oversimplification. But all this gets us into technogeek territory!
Basically, I think JoeE is right: it's irrelevant as long as the implementation is competent. To risk some oversimplification of my own, using MOSFETs is a tradeoff...just like every other engineering solution to a problem. Manufacturers who play up the use of MOSFETs are just indulging some audiophiles' prejudices and bandying technical jargon about for marketing purposes.
And no, you don't have to use a bipolar transistor amp with bipolar speakers...
