A new Control Ultimate Edition PS5 and Xbox Series X console comparison video shows that one console seems to have a slight advantage over the other, but you can hardly go wrong.
Digital Foundry went in-depth with the newly released new-gen version of Control to compare their graphics and performance across all consoles and supported graphics modes. The good news is that, whatever console you own, this new version of Control Ultimate Edition is going to look very good on them, whether you play in Performance mode to stick to 60FPS or Graphics mode to enjoy all that beautiful ray tracing - Performance mode is the default option, and also the only one available for Xbox Series S.
According to Digital Foundry's testing, PS5 does have a slight advantage in sticking to a stable 60 FPS when playing in Performance mode. Oddly, the problems on Xbox don't seem to be related to intense combat-related effects (which can cause both consoles to briefly dip into the mid-50s instead), but instead to hitches that can occur when moving through the environment, when cutscenes start, or even when the big location names appear on screen when you first set foot in a new area. Remedy is already looking into the issue, so it's possible a future update will render the performance across PS5 and Xbox Series X nearly identical.
That's the case for Graphics mode, which appears to run just as well on either console. DF noticed that the PS5 and Xbox Series X versions have occasional frame pacing problems, which means they may look a little jittery now and then, but they're rare enough that the built-in motion blur largely covers it up.