Nothing is missing - the content that was in the original game is still in the HD release. It's just that (as we assume) when the team was working on the remaster, they no longer had original game assets (backgrounds) in high definition so they had to work with what was already prepared for GC release. So in order to prepare backgrounds for 720p/1080p release, they mostly just resized them and applied a ton of filters (some rooms were completely redone in 3D, and animated elements were turned into 3D objects). This resulted in some rooms looking pretty good (e.g. the main hall) and some looking terrible (every single background from the Aqua Ring area).
With Zero it seems they have all original assets and thus were able to properly prepare them for HD release. Backgrounds are good looking and sharp, as if they were rerendered in high resolution - no resizing and artistic filters there. You can also see that cut-scenes are now running in widescreen, meaning there are portion of backgrounds that were not visible in the original release.
I think it comes from the first trailer:
https://www.youtube.com/watch?v=oKloGAjT7qs: REmember, REality, REbirth.