The 1,4GB difference between an MP4 and AVI of the same movie is 800kbit/s on video and 20kbit/s on audio. It also seems like the color is a bit different, maybe due to unrelated factors of movie origin (DVD, B-RAY, WEB), yet the level of detail is untellably similar. So in the case of size, MP4 is undeniably the winner.
This can however change depending on the codec used, I wrote a post earlier about DivX or XVid, and though they are currently the most popular codecs, there are plenty with much higher compression rates for .avi files. h264 is a great codec with a high compression ratio that is quickly gaining popularity, especially within the fansub world it's used commonly due to it's ability to pack a lot of quality in a small file size. Generally computers won't have any trouble playing files using any of these codecs, but as an encoder you'll need a pretty powerful CPU (or lots of time) to use this format, which may be a reason why the format still isn't as widespread as it should be ... considering how good it is. Or maybe that's just because the older codecs are supported by more media players. x264 is another high-compression codec, btw.
For those of you new to codecs, here's a simple explanation.
'Codec' is a technical name for "compression/decompression". It also stands for "compressor/decompressor" and "code/decode". All of these variations mean the same thing: a codec is a computer program that both shrinks large movie files, and makes them playable on your computer. Codec programs are required for your media player to play your downloaded music and movies.
AVI is just a container format, as is MP4, but the different container formats still use different codecs. DivX and MP4 for example don't go together, and is the case here most other codecs only work with one container format. Using the codec with the best compression for each filetype and otherwise retaining the same quality MP4 still wins the race, it's newer, it's better built, and actually I'm just speaking nonsense. MP4 and XVid go hand in hand I realize after a quick Google, so forget everything I said so far, it's all about bitrate, the filetype doesn't matter at all.
I think I need to do some more research. Later.