They're different containers, not different codecs. For the average user that means absolutely nothing and shouldn't affect the A/V quality.
What affects the quality is the codecs used. Both MP4 and MOV usually contain the MPEG-4 codecs, which includes AAC and H.264. Other codecs include Xvid and DivX but they're rarely found in anything other than AVI containers.
In terms of quality you should find that H.264 is the best for overall file size and visual clarity. You need a more powerful computer than the others however. Any modern Mac within the last 2-3 years can play SD H.264 videos just fine.