Here's the thing: console gaming isn't pc gaming.
For one, a lot of games are rendered at 720p or less (and then upscaled). It really doesn't make a whole lot of difference between the 720p and 1080p setting. You'll get a higher res menu, but that's about it (that and 1080p video content). But strictly from a gaming perspective, you wont see a difference between 720p and 1080p.
Second, AA isn't really present on consoles, at least not on a wide scale. A good majority of games will have jaggies, and that's just the way it is. A lot of people won't notice the jaggies on a 40in TV while sitting on a couch a few feet away. You will notice them, however, on a 24in monitor just a foot away. Textures are also much lower than PC games.
The truth of the matter is, if you're going to do console gaming on a pc monitor, you're gonna have to lower your standards a little bit, because it simply won't look as good as you think it will.