Any game (older, unpatched XB1 games, or emulated 360 games) can potentially see improvements from the faster hardware on the X, if it's not running at a steady framerate, or uses a dynamic resolution scaler. There's no throttling of hardware or anything to try to match an older system's limitations and specification (beyond possibly anything that may be necessary to get the 360 emulation working at all).
A handful of titles, Oblivion being one of them, run on an updated emulator that lets them override render target/framebuffer sizes so they can bump up the resolution to take full advantage of the X, by running at ~4K (technically it's running at 9x resolution - 3x wider and 3x taller than the original, meaning native 720p games hit 4K, but anything that was sub-native on 360 will be proportionally sub-4K on the X).
That's only available to a small number of titles so far, though, as there are some technical limitations on what games it can actually work on, and requires more work by the back-compat team (the implementation is tweaked manually for each game, with some getting additional benefits beyond the pure res boost, such as Assassin's Creed getting the shadow resolution boosted as well). And while they haven't said anything officially, I'm betting that they're being cautious (and probably seeking approval before going ahead) to avoid stepping on publishers' toes regarding potential remasters.
The OG back-compat titles are worth noting too - on the S, they run at 4x resolution (1280x960 for native 480p games, which was most of them), and on the X they run at 16x (2560x1920). And in this case, that applies to all of them - they're all enhanced on either system, the X just takes it further.
