Its all about perception. I can see little details that some of my friends cant.
To me, if its on a 17" monitor (CRT) then 1280x1024 is the max I can see detail. Anything higher and I cant tell the difference. On a 19" CRT I like to run games at 1600x1200 if possible.
Its generally better to run at a higher resolution than to turn on AA. (You are correct about AA). But if you got an older game that will only go so high, then it definately makes an improvement.
Dungeon Keeper 2 only runs stable at 800x600. But with 6X anti-aliasing even I have a hard time seeing pixels on a 19" display.
IF you were to go all out and get a 22" monitor, than I would recommend moving back a little.
Also, if you have an ATI X600 or X800 then you can play the Ruby demo. On that you can tell a difference with AA. Even 2X AA moves it from a really good 3D computer demo, to a movie quality experience.