I can't believe that this was done 2½ years ago...Beo, you're an old man
If you're looking for anime itself that uses rap music, check out Samurai Champloo. As for rap in AMVs, it does seem to be different trying to edit to rap as opposed to rock or pop, let's say. Lyric sync is harder, because not many anime have scenes in them that can relate to rap lyrics, unless you're going for a cheap comedy. You don't want the video to degrade into just lip syncing, and beat syncing get kinda hard too, because most everything is just repeated. It takes a good rap song to make a good rap AMV, and by good rap song, I mean one that can be used (has story, variety, something), not saying that most rap sucks.

