For Mortal Kombat 11 Ultimate on Xbox, it has less input lag then PlayStation 4. As someone who plays the game on PC - Steam, Xbox Series X, and Xbox One X, there's no major difference in terms of performance outside of the 60 FPS Intros and Fatal Blows, since you can connect your Controller to the console via a USB cable and it becomes a wired Controller, something PlayStation can not do. PlayStation 4, the tournament standard version of the game, is actually one of the worst places to play it on.
For Mortal Kombat 1: Khaos Reigns, I only play on Xbox Series X and offline, and I've had no performance issues either.