There are a ton of shoot outs of both phones in Youtube.
The difference of quad 3rd generation cores vs. dual 4th generation cores in performance don't seem to be much in real time perception. Neither is their power benefits, but do note that single and dual cores of the previous generation don't hold an advantage in power consumption over the latest chips.
While the Galaxy S3 does have a bigger, removable battery, the One X does have a number of built in power saving tricks of its own. The Tegra3 especially, is a power miser in standby mode, as my experience of it in tablets.
I personally think the S3 has a slight edge over the One X, but its not the knockout the previous generation S2 had over its Sensation rival. This one goes down to the judge decisions and personal tastes, subjective feelings can decide the matter for you.
I am @guamguy on Twitter.