This is an interesting question
Things like Yakuza and the like felt a little funny on Xbox at first, but once you're playing it's absolutely inconsequential. It's easy to forget Xbox very much has the DNA of Sega.
There's some titles like Metal Gear Solid, Spyro, Tekken, Crash Bandicoot, Persona, Silent Hill that are so PlayStation that I can't imagine them having anything but a Dualshock. What's super interesting is I wouldn't bat an eyelash at HZD or Uncharted hitting Steam.
As for titles that feel most at home on Xbox, I'd say things like Mass Effect, Fallout, Elder Scrolls, Cuphead, Ninja Gaiden, Splinter Cell (and to a mild extent Call of Duty) really established themself on there.
There's some that feel completely device agnostic now, I'd say Final Fantasy, Resident Evil, Minecraft, Sonic the Hedgehog, Street Fighter, Grand Theft Auto don't really raise an eyebrow on whatever platform they choose now.
But of course more good games should be available to everyone and it's a generational thing.