The SGSIII is the much better choice.
It has a Super AMOLED display which produces much more vibrant colors, has superior contrast and deeper black levels than LCD.
Also the SGSIII US Version has 2GB RAM compared to the HTC's 1GB RAM.
The SGSIII clearly outperforms both the HTC One X and the iPhone 4S in benchmarking tests. The SGSIII is much more optimized and is much smoother and responsive than the other phones.
The SGSIII also has a superior camera. The HTC One X can't even record video at 30 FPS.
Furthermore, the SGSIII has much faster 3G/4G LTE transmission speeds. The HTC One X often has the WiFi death grip problem which means that sometimes you can't access the Internet. HTC has had a lot of problems with their QC issues.
So the SGSIII is the best phone to get.
You should also consider the Note 2. Basically bigger and more powerful than the SGSIII and has added functionality.