I think the screen on both looks good actually. Sure the, LCD2 looks sharper when viewed closely, but there's just something about the AMOLED screen on the S3 that looks great (no, not the over saturated colors), but the fact that it looks more like a plasma screen in some regards. It's softer, and "snappier", in lack of a better word.
Watching a movie on the HOX is a bit of a bummer (overstatement, lol) after trying it one the S3. The one in the S3 definitely looks better than the one in Note and the Nexus though. Also, the use of Gorilla Glass 2 seems to help making the screen brighter.
I guess this whole thing just comes down to personal preference. I would've liked the screen in the HOX a lot better i you could adjust the sharpness, and the S3's screen would've been the business if it didn't use Pentile technology.
Now, people stating that one is tremendously better than the other, I don't understand. A lot of people here come of as faboys or a bit sore that they are stuck with either one of the phones. News flash: Sell/return it and get the other.
And are we really that spoiled that a 720p Super AMOLED HD isn't sharp enough? Or that the blacks on a LCD2 isn't deep enough? Come on, now we're just nit picking.