ferrouslepidoptera's writeup is very accurate being based solely on fact, while leaving out any opinions to do with sound.

One reason that people may favour tube amps to transistor amps is because of their effect on the sound. Because a transistor amp produces sharp corners on a distorted signal and a tube amp does not, a transistor amp's sound contains the higher harmonics of the input signal in far greater degrees than would a tube amp.

Now, to break away from the sound of the guitar, take for example the sound of static, as can be heard by an untuned radio or television set. This sound (in theory) contains an aggregation of all frequencies, and so it sounds like unintelligible garbage.

With transistor distortion, the abundance of high harmonics creates a sound that is very reminiscent of static, because of the high frequencies present. Proponents of tube amps favour the tube sound because they dislike the sound of static that transistor amps often remind them of.