There's very little difference between the One X and One X plus, and the only thing of real note is the increase in processor speed.
Anyway, most of the lag that you MAY be seeing on high end Android phones could be attributed to the UI software. Maybe the SIII you got is in bad need of an update for the stock launcher. However you can always change the UI software into something smoother. These are called launchers on the Android Market. Heck my 2 year old Galaxy S is still as smooth and no lag on the UI after all this time, I just changed the launcher program.
I would personally pick up the SIII or the One X/X+