Every 360 game will get improved texture filtering (forced 16xAF), and the higher performance will give higher framerates if possible. Dynamic resolutions weren't common last-gen, but I'd imagine that any games that do use it (RAGE did, I think?) would also benefit similarly to XB1 games (except still probably capped at 720p).
A limited number of games see bigger improvements, with resolution increased to 9x the original pixel count (horizontal and resolution both increased by 3x, so up to full 4k for games that ran at native 720p), and some further tweaks to improve the presentation of the textures (they're not adding anything to the games, just doing what's they can at the emulator level so that the best quality versions of the existing textures are used and looking as good as possible).
So far the latter enhancements are only available for 7 games - Assassin's Creed, Fallout 3, Halo 3, Oblivion, Gears of War 3, Skate 3, and Mirror's Edge.
edit: And OG Xbox games run at 16x their original resolution (4x4), rather than the 4x (2x2) that they run at on the original XB1/1S, so a 480p game will be running at 2560x1920.
