It all depends on what you want to do with your video and what you are using to capture it.
Use AVI if you are going to be editing the video heavily (anything more than removing commercials). Editing programs such as Adobe Premier prefer AVI and handle it much easier and faster than MPG. If you are going to be converting to another format (DiVX, etc.), then AVI is the way to go as well. Use AVI for video you want to process through programs and filters such as Virtual Dub.
Use MPG if the final result is going to be a DVD. MPG also works well if you are going to use TMPG to process the video and remove noise and/or correct color. Keep in mind that every encode/re-encode of MPG video will reduce quality. That's why it's best to start with AVI for heavy processing and work down to MPG. Good MPG capture cards (such as the ATI All in Wonder) will do a lot of processing and filter for you in the capture process. They also (when correctly set) create DVD compliant files that can be imported directly into authoring programs.
and read up for more detailed info behind what each format is good for.