I have a large collection of .divx movies. And I have watched .avi. DIVX is the clear leader, IF the source is good. DIVX is also burnable to DVD or CD if your DVD player supports DIVX. They look great on my 55" Sony SXRD.
The down side is that while DIVX is the better format, it's hard to find DIVX movies.
What's the difference, and how does it play out?