It looks like Radet covered most of this pretty well, but to summarize everything:
- Xbox 360 games (on backwards-compat list) run at native resolution on Xbox One/S. This is usually 720p, but can technically be higher/lower.
- ^ X360 games do receive a nice framerate bump and loading improvements in almost all cases. A game that might have had dips to 25fps on X360 hardware will most likely remain locked to 30fps on Xbox One/S
- X360 games, on backwards-compat list & enhanced for Xbox One X, get a 3x resolution bump and forced-on 16x anisotropic filtering. That 3x bump from 1280x720 results in 3840x2160/native 4K. The 16x AF helps clean up textures quite a bit.
- ^^^ On top of that, X360 games enhanced for Xbox One X generally have even more of a performance boost. It's pretty rare to see them drop frames.
Microsoft has already confirmed that all Xbox/Xbox 360 games that run on Xbox One/S/X will continue to run, with further performance boosts, on Xbox Series X coming holiday 2020. Xbox Series X will also run all current and future Xbox One/S/X games, and most likely will run Xbox One/S titles in particular at a higher resolution/performance boost as well (i'm not expecting much though for games already enhanced for Xbox One X).
Above I referred several times to the backwards-compatibility list, here is the link to that: https://www.xbox.com/en-US/xbox-one/backward-compatibility
That page shows every original Xbox and Xbox 360 game that can run on the Xbox One/S/X, and you can filter it by Xbox On X enhanced titles as well. It's a massive list - 607 titles total now(!!!). Microsoft has done a really, really good job on getting their older system titles running on current-gen (and future-gen) hardware.
