I had CM 10.1 on my S3 and everything worked fine (besides LTE) but I just didn't care for it (though it's certainly better than stock) so I started looking for another option. I decided to try the Sprint build of LiquidSmooth 2.9 since that's what I run on my Nexus 7. It works great! I don't know about LTE since I don't live in an area that has it, but everything else does. I also had to flash the MMS/voicemail fix that I modified from someone else's fix for a different Virgin phone (I can't remember which, but my fix, in which I merely fixed the mount points for the partitions) can be found in the CM 10.1 thread.