AVI is just a container format and could conceivably hold anything from low-res MPEG1 video to high-res MPEG4 encoded video. Windows Movie Maker 2012 already supports two formats (.mp4 and .wmv) that can store compressed video up to HD (1920 x 1080) resolution without problem and that's about the highest you can get.
I think the misnomer here, and it may be from the days of SD video, is that AVI is a higher resolution format. When we had SD camcorders that recorded in DV-AVI (720 x 480), that resolution was pretty good. What made it good was that it didn't have a lot of compression, so it was closer to a "raw" format. It also was an order of magnitude larger in file size compared to compressed formats like .wmv which was a disadvantage.
However, in the prior versions of Movie Maker (e.g. Movie Maker 2.1 from XP), the DV-AVI output choices for SD video could mean a perceptibly better picture compared to the alternative .wmv output. However, this difference goes away when you talk about today's modern HD video. The current HD encoding in WMV format (in a .wmv file) or the H.264 encoding (in a .mp4) format gives you both high quality video with a good balance for file sizes. If you were to take HD video and encode it as DV-AVI you'd actually be losing resolution because it would have to be 720 x 480 rather than a possible 1920 x 1080.
I can understand your wanting the best resolution possible and I believe the .wmv and .mp4 options do deliver on that. In fact, you'll see H.264 encoding used from broadcast networks, to cable companies, to online websites, to portable devices, to Blu-ray players. You cannot say the same for the old DV-AVI standard which might have been fine for its time but is definitely outclassed today.
In any case, if what you want is an Xbox friendly format, do as PapaJohn noted and change the output of your movie from the default of .mp4 to "Windows Media Video" (aka .wmv). Then you'll be able to work on devices that can't handle .mp4. Alternatively, there are converters like Freemake Video Converter that can output to additional formats if .mp4 or .wmv don't meet your needs.