I did a back-to-back comparison of Phantom of The Opera HD DVD vs. DVR'd version off HBO-HD on E* (and vs. standard DVD too). This is not a very accurate comparison, as the HBO's version is not in OAR (it is cropped to 16x9), but that's the best I could do.
Since I only have one HDMI/DVI port on my TV set, I first connected both the HD DVD player and the 942 DVR via component cables, synchronized both video streams and was simply switching between the two throughout the movie. I then connected via HDMI and watched one copy at a time to re-confirm my observations.
I must say, the difference was striking! Much better than I expected. I didn't realize the PQ on HBO-HD was so bad in comparison. Yes, I knew the HD picture was not perfect, but in the past I attributed some of that to limitations of my TV set (Sony Grand Wega III). Suddenly, I saw that my TV can do much better!
So, what exactly is better on HD DVD compared to HD off E*? Both offer similar resolution, but the picture on E* has a lot of compression artifacts. First of all, pixilation, especially in fast action. I saw pixilation in many scenes of The Phantom (HBO). But I am yet to see a single case of pixilation on any of the HD DVD titles. Colors, color-gradients, skin-tones - all look much more vivid and natural on HD DVD. You get almost a 3-dimensional effect. In comparison, the HBO version looks flat and washed-out. (I thought it looked great, until I did this back-to-back comparison with HD DVD!)