.AVI is outdated. AVI doesn't support VBR audio (actually AVI specs do support it, but software using ACM to read audio from AVI files will not be able to handle VBR audio streams correctly, even though such files are compliant to the AVI file specification).

If your .MOV file contains AAC audio with variable bit-rate and you don't the AAC audio to be converted, you can use other containers for MPEG-4 video: MP4, MKV, OGM.

.MOV container is based on .MP4. And it seems like you can safely rename .MOV files to .MP4 in most cases.

But Apple always like to create standards not supported by other software and hardware. No wonder QuickTime 7 added support of multichannel audio (used, for example, in the high-definition trailers on Apple's site) to .MOV container while the original MP4 container is limited to stereo only. Therefore multichannel audio must be re-encoded during MP4 export.

In the MPEG-4 Export dialog of the QuickTime Pro use an option called Passthrough to do a .MOV lossless conversion (export) to .MP4 without affecting the audio or video streams.