My brother would like to switch from a PC to a Mac but he has a problem with all the movies he has created in MPEG format. He is looking for a good converter that would not affect too much the quality of his movies. He is telling me that all the ones he has tried so far yield a very poor quality movie after conversion. Any suggestions?

I have the feeling that he did not set his conversion parameters properly. But does anyone has a particular converter she/he recommends for quality of conversion?

http://ffmpegx.com/ which is an ffmpeg GUI.
Converting usually does not make sense though, since you will always lose quality. Except if he chose a very rare (non-standard) codec …

The problem is that you don't give enough information here.

MPEG can be really anything, four containers (including mp4) and also four codecs...

What most people call "MPEG" is actually mpeg2 video in an mpeg program stream container. You should be able to put that in an mp4 container (!) without re-encoding and also without quality loss as a result.

FFmpeg does it like this: ffmpeg -i MPEG_file -vcodec copy -acodec copy -f mp4 MP4_file.mp4