HD-DVD supported H.264 and VC-1 (and MPEG2). Initially there were plenty of VC-1 and MPEG2 releases on Blu-ray as well. HD-DVD simply died before the universal shift to H.264. There was however a difference in max. bitrate (~40 Mbit/s for Blu-ray, ~30 Mbit/s for HD-DVD)
The differences between the two standard were more interesting when it came to sound formats. HD-DVD had mandatory support for Dolby Digital Plus and Dolby TrueHD (allowing the audio on a disc to use these without a fallback). Blu-ray on the other hand supported a higher max. bitrate for DTS-HD Master Audio.
Bluray menus are Java, and HD-DVDs' are JavaScript/XML https://en.wikipedia.org/wiki/Advanced_Content
HD-DVD uses Microsoft's WMV3/VC-1. Bluray (non-UHD) supports both AVC (h.264) and VC-1, but AVC is more common https://en.wikipedia.org/wiki/Comparison_of_H.264_and_VC-1