Standard DVD's are limited to 720x480 resolution. HD-DVD will most likely be either 1280x720 progressive, 1920x1080 interlaced or 1920x1080 progressive. Simply put, on High Definition displays, HD-DVD will be far more crisp and three dimensional looking. Hopefully some new higher bit rate sound formats will come along with it.
I'm hoping for 1920x1080 progressive as it's easier for the hardware to downsample to match the resolution of your display than it is to upsample it. Fewer artifacts this way. Most current HD displays are either 720p or 1080i. A 1080p DVD player could easily downsample and output either of those resolutions while at the same time upsampling standard definition DVD's to the native resolution of your display. Upsampling a standard DVD doesn't yield a true HD image but it's noticably better than not upsampling, and especially so if you're using an all digital path (such as a DVI output from your source to a DVI input on your display).
Some displays are already heading toward native 1080p so I think that would be the logical choice for HD-DVD. Who knows what will actually happen though.