In-game, Mewtwo would definitely win. It's got better Speed stat, heavier defenses, stronger offensives, and more HP. It has access to plenty of moves as well, and after only just one use of Calm Mind, it would become nearly impossible to stop. Whenever its health gets low, it could always restore itself instantly with Recover. Mewtwo might be super-effective against Darkai (since it's a dark-type while Mewtwo is psychic), but still—it would definitely be the victor. In anime, though, I'm not exactly sure who'd win. xD They would be equally as strong probably, so I'm guessing it'd be a tie?
I think Mewtwo would win. As dark and powerful as Darkrai is, Mewtwo is engineered to be an ultimately strong pokémon with psychic powers almost unimaginable. I don't know about their game stats, haha, but I believe Nymphadora and always thought Mewtwo - as a proper "legendary" - probably has some of the best stats overall.
If you, outside of the games, do take into account that psychic type attacks don't affect dark type moves though, things become trickier. Perhaps Darkrai could lure Mewtwo into defeat after all.
Without having any knowledge on real battling I would say Darkrai, simply because of the type advantage.
But now that we've also got Mega Mewtwo X which is also a Fighting type that disadvantage shouldn't be a problem anymore.