Heh, funny post topic... something I went through myself about 6 mos ago.
The choice is easy, actually - buy the movie first. Not only is it an excellent film, gorgeous in sound an photography (by an all-star team of cinematographers), but it's got two exceptional commentary tracks. The first, by Marty C and Robbie it fun, certainly the reason I was excited. However, the second commentary, by everybody from Ronnie Hawkins to Levon Helm to Irvin Winkler (who never even saw the film!) is a total blast, and a really big surprise.
The 5.1 is really good, and the pic is top notch.
Now, if you are a big Band fan, you'll probably want full versions of the songs, and the DVD-A is certainly really nice to listen to. It's 48khz 5.1 - not a huge leap from the DVD, but with additional performances and the added sonic clarity it's definitely worth owning. If you're silly, there's also the 4 disc CD boxed set that's got the entire show (the DVD-A is an edit from this set). In an ideal world, I'd have rather had a 2-disc DVD-A with all the tunes on the 4cds. But, hey, you can't have everything, and the format's struggling as it is...
Anyhoo, that's my thoughts - you'll enjoy whatever title you buy.