Right, so first thing to note is that Magic Bounce will not work more than once. Once a move is reflected back, it can't be rebounded back again. Second, thanks to both Pokemon having Synchronize, if any of their moves results in a major status, such as Paralysis, then the other Pokemon will receive that status as well, regardless of Magic Bounce. However, both of them also has access to Refresh, which cures status conditions, so this maybe somewhat moot.
Second, there's type advantage moves on either side. While Espeon has Bite, which can flinch, Xatu has both Sucker Punch, a priority move, Feint Attack, a move that almost never misses, and Ominous Wind, which has a small chance of boosting all of Xatu's stats. Plus, unlike Espeon, it has Me First, which can allow it to use something like Bite on Espeon in case it does try that. However, Espeon is the only one who has access to Detect, which can allow it to perfectly avoid any attack that Xatu attacks it with, regardless of perfect accuracy moves like Feint Attack.
Both of them has access to immediate healing, with Espeon having Morning Sun and Xatu having Roost. Though, Xatu also has access to STAB moves such as Drill Peck and Air Slash as well. And then, there's Tailwind, which does helps Xatu with its maneuverability and speed.
Overall, while both of them are decently similar, and this would be an extremely close match, I just see Xatu having just a few more tricks over Espeon, plus it has a little more insight in the future than Espeon as well, if the magnitude of the Pokedex entries are to be believed. So, I'm going to give it to the mystical Box Opener with very high difficulty.
Winner: Xatu