Throwing bias out as much as I can... (even though a lot of the posts in this thread are all total bias)
I'm currently using the Galaxy S3 (sprint). I'm on edge on whether to keep this one, or get the One X variant on sprint.
Build quality, hands down, goes to HTC on this one.
The battery, so far, is on the S3.
The screen, for overall through-the-day use, goes to the One X, easily.
Speed wise, I can't tell a difference between the floor model and my S3.
Development seems to have taken off a lot faster for the One X, as well. Not sure how long before we start seeing non-stock based roms for the S3.
(bias) As for the overlays, I'm more preferential to the One X again. The TouchJizz--Touch Wizz interface -cough-sorry-cough- just looks toony and cluttered to me compared to Sense which looks like it's matured. Really don't like it. The faster cyanogenmod is released for the S3, the better.
Camera is definitely to the One X. Image sense tech is awesome, and it shows in the pictures. Video is also clearer.
I'm still in debate. Got till the end of next week to figure it out.