I have not handled the Sammy S3, so I cannot compare to that specifically, but I really love my T. I've owned quite a few HTC devices (and the Mrs has a One), and I have to say I think the Sony 'feels' much better. Their homescreen is the best one I've found (it's not overbearing like Sense), and they keep the crapware to a minimum.
Screen is nice, it runs games like a champ, and it takes MicroSD.
I really don't have any issues with mine, and have been running a custom ROM since I bought it in November.
Additionally, if you're looking into rooting modding etc... Sony is definitely working to tip the scales in their advantage. They have been releasing source code for much of their work, making it much more friendly to the mod community.