Like Chocofingers said, you can read the detail on web. But in current radio broadcast, the difference is more the regulation than the nature of the AM and FM. For example, the AM band limit the upper limit of frequency of the channel to something like 5KHz, you can get hi-fi out of this. FM is more like 15KHz, don't quote me on the exact number. AM don't not allow stereo and that make it even worst! That is the reason you don't really listen to music on AM.
From existing bands, AM is in much lower frequency, maybe that is the reason they put all the limitation to limit the side band to avoid breading over to the neighbor channel. The upper frequency response imply the side band spread from center frequency ( eg, 810KHz for a station ) to +/-the frequency response. So the higher the frequency response, the wider the frequency the channel is and you can put less channels in the given band. Stereo funther increase the band width.
You should read into AM and FM modulation and look at the side band characteristics to get more insight too, I have not read it for a long time, I am sure I missed a lot of other stuffs.