It downconverts. Bit its important to remember that officially 720p isn't inferior to 1080i. The heirarchy for resolutions on televisions is:
480i - normal standard TV resolutions. Most consols. VHS tapes?
480p - Xbox progressive scan titles. DVD movies
720p/1080i - Various types of HDTV, with CRT projection sets normally albe to do both, and most HDTV plasmas and LCDs able to do 720p.
1080p - best current resolution, but basically no content.
As you can see above, most people buying plasma TVs right now, even if they spring for the HDTV models, aren't getting the max resolution possible. This is why I have waited to buy a next-gen television - even the CRT models don't normally support 1080p, and I have a feeling many of the current purchasers are going to be left with inferior sets five years down the road, while 1080p sets might stick around for a while.