I'm going to assume that you mean you have a Movie in Photo-JPEG codec (yes it IS a valid legacy Quicktime Format), and would like to convert it to MP4. Compressor simply uses the Quicktime Engine, so as far as sync goes it will be no better or worse than anything else (i.e. FFMPEG or anything that uses that specific engine). Like @georgi.m said, stick with common frame rates and sample rates.

Bear in mind that Photo-JPEG is an INTRA frame codec, while MP4 is an INTER frame codec, which means that rather than individually compressing each frame, the movie is compressed in Groups of Pictures (GOP). Essentially the start, middle and end of each GOP is compressed and then the frames in-between are interpolated (oversimplification, but gets the gist). The end result is much lower data rate for a given picture. However the tradeoff is that the CPU (as opposed the the Hard Drive) has to work harder to decode the movie. The other tradeoff is that the Audio and Video streams are decoupled for decode than re-integrated on the playback. In theory this works fine, but in practice, a slow computer or slow connection WILL result in sync being off (it taking longer to decode the video than the audio). This has NOTHING to do with the program used to encode the MP4, and everything to do with the computer playing it back.