Ok, A few small things need to be addressed.
First off, No matter how good they look, Mpeg 4 is never higher quality than mpeg 2.
Raw uncompressed DV is converted to mpeg 2 as the standard for DVD video. These ae seen as .vob files on a DVD, but they're just mpeg-2 files with a different name.
All mp4 files start off as mpeg-2 almost without exception. Even professional video equipment records in a compressed format most of the time, so even if you're coming from "the source" it's still most likely starting life as mpeg-2, and sometimes with the newer consumer cameras, straight to mpeg-4.
That being said, compression will never yield a higher quality result than the source. it's impossible. It may be close, and with de-interlacing, and smoothing, it may appear glossier, but it's actually the equivalent of using a blur tool in photoshop to cover a jagged edge.
All MP4 files are simply AVI files. so are DIVX, and MKV, H.264, and FFDShow, and others... They're mp-4 files also,and also AVI's. MP4 is not the encoding type, it's simply the compression standard that whatever particular codec you used is following.
AVI is simply the container file. An AVI could be encoded, and potentially contain any one of over 80 codecs in the wild right now. This is why often when someone goes and encodes their video collection, then shares a file with you, it doesn't play on your machine. Most of the cheapo video conversion softwares use a variant of a more mainstream encoder, hence making playback of the file incompatible with your software without inclusion of yet another software.
The trick tocompressed files is that they're inherently lossy, so you want to remove as much info from the data stream as you can without it becoming apparent as to which data is missing.