What do you think a fight between two time travelers would end up like?

Ignoring technology? Not that special. As we’ve said many times, martial arts adapt and evolve to the current combat climate. With no shared climate, whichever one had an advantage would probably snuff the other in short order.

Time traveler is kind of it’s own occupation, which throws a monkey wrench into picking up multiple styles, you just wouldn’t have the time… unless they’re also immortal. And even if they do, marital arts training does atrophy from disuse, so the twenty years your time traveler spent learning a new style would actually make them worse at a style they’d learned earlier, simply because they couldn’t practice it openly without creating some kind of paradox.

If they’re immortal, or have some kind of advanced future technology that makes them invulnerable, or guns that fire plasma, or mind control nanites that force marmosets to do their bidding, or… whatever. But, that’s more of a “who has the best toys” kind of question.