For 2010 I would have to give it to Heavy Rain. Everything about this game is just about perfect. The graphics were amazing, especially on the character's faces. The voice acting was just about perfect, although the voice actors for young Scott and his brother and Ethan's kid's weren't that great. The story was gripping, and the gameplay was exciting. Any flaws in the game are quickly overlooked once you start playing. The music did a great job of setting the mood. Plus a story where your choices can influence the outcome of events makes for great replay value. And the game gives you a cast of characters you feel for. I just wish the game was longer, but any great game should leave you wanting more.
For 2011 I'm torn between Dissidia 012 Final Fantasy and Solatorobo: Red the Hunter.
Dissidia is probably one of the best fighting games I ever played. The graphics are nice, although the story mode was too easy. Some fights lasted less than 30 seconds. But there is plenty to do and unlock. And the game has enough modes to keep you coming back for more. The enemies can be very challenging, but that just makes it all the more rewarding when you win.
Solatorobo had some of the best graphics I've seen on the DS, the music was great and fit in perfectly. I liked the story for this game. Just like with Heavy Rain, Solatorobo gives you a cast of characters you care about and feel for. There's plenty of side missions in this game. Although a lot of the missions require you to do the same basic thing, like fight, it never seems to get tiring. The dialogue can be pretty funny at times. The game is colorful without feeling too kiddy. Plus there's more missions that open up after you beat the game. And more robots become available when you start a New game +. The gameplay is a little simple, but it's fun. And the mini games are enjoyable.