The big difference is that Blu-ray is supposed to be able to support up to 50gig per disk while HD-DVD is limited to 30gig.
They both have quite a bit of DRM in them, though a big reason Microsoft chose HD-DVD over Blu-Ray because there is alot more of it in Blu-Ray, not because Sony developed it and they compete in games. As I understand it, Microsoft thought they were going overboard.
Another big reason is that HD-DVD disks can be made using existing manufacturing facilities with relatively minor, and relatively inexpensive changes to the existing facility. The drives are much cheaper at this point as well. Blue lasers are not easy to make apparantly.
I think the only issue with the Microsoft drive, and the XBox is that it doesn't have an HDMI interface, which will become important when the studios start enforcing the use of HDCP. I'm OK with that as the plasma set I got 3 years ago doesn't have an HDMI interface and I won't be buying another set for 5 years probably.
The $200 for the XBox drive is a steal if you already have the XBox, and the component output is excellent.
Quality of image is indistinguishable between the two.