This is mostly from what I've read, and not really from personal experience, but apparently the AVI demuxer in QuickTime is broken in such a way that AVI files with VBR MP3 audio have horrible sync problems. This has been reported again and again to Apple, and they won't fix it, leaving most people assuming that it is intentionally broken to discourage the use of AVI.

So I've decided to be discouraged from using QuickTime.