I'm not a hundred percent sure but I don't think you can do anything about resolution in 360 games. The designers program the game at a certain resolution, and that's that. Changing your display's resolution won't make any (or very little difference). I play on a CRT monitor with VGA and I get horrible jaggies on Divinity 2. But I've also played a few other games on a full HD 1920 x 1080 monitor with HDMI and it made little or no difference.
I've also played games on a 32" LCD TV and I still get jaggies.
And I've also played games on that CRT monitor with VGA and got no jaggies at all. I can only assume it's just the way they program the games. They set the resolution, and apply AA, or no AA. If you could change the resolution there would be options for it in the game's settings like on a PC game. But there aren't.
Like I said, I'm not completely sure about that, but from a bit of research and a good deal of experimentation that's the conclusion I've come to.