Metal Gear Rising: Revengeance is a much, much, MUCH better game. This game is completely derivative, casual, and plays itself half the time. Metal Gear Rising is developed by Platinum games, has a unique gimmick and a really well designed battle system. It's not even close.
No, since you told me to shut up, I think I'll talk more. Thanks for asking.
Tomb Raider is simply not a very good game. As a shooter, it's okay, but not particularly challenging. At least it controls smoothely. But it's a very derivative game. You can't compare that to MGS:R which has a totally unique and innovative mechanic, which the entire game is designed around, which creates a fresh new experience.
If we want to talk about stories, both games have pretty bad writing. But personally I prefer MGS's more for being quirky and outrageous, at least it's interesting at times. Tomb Raider's story is a vapid attempt at mimicing vapid Hollywood movies. All the characters other than Lara are as shallow as Hell, and nothing happens in the game that isn't overwraught or predictable.
Regardless of opinions right now, I'm quite positive that MGS:R will be the historically more important game. In the future when games include more ways to dynamically damage an enemy, they'll look back on MGS:R as a stepping stone. No one will look back at Tomb Raider 13 as a stepping stone towards anything except mediocrity.
I just got this game and so far it's a lot better than I thought it would be, definitely one of the better releases this year. I played the demo and watched lots of videos for MGR and it seemed really boring, the 'completely awe-inspiring innovating slash bro fest' that guy up there is praising is nothing but a gimmick and it doesn't work well at all, I was tired of it half way through the first battle.