Heh...don't exclude Logic Audio, either.
If you're talking about composing.
Ok, Videowise, basically it's like this...Premiere you can add audio and do basic editing. In, After Effects you have more editing control than in premiere. You could also check out Sonic Foundry's Vegas, as well...which is kinda like their version of AE...heavily geared towards audio (they make sound forge, after all)...supports surround sound, etc.
Like KB, suggested, if the music portion is the primary concern, you'd be better off with something like Nuendo, Cubase, or Logic which allow you to work with video....though from some of the user forums for both Cubase and Logic, at least, there have been quite a few problems.
EDIT: I should've read Dexter's post better....he said it all.
"Terminat Bora Diem, Terminal Auctor opus."