I installed CM10 (Jellybean build) on my Sprint GS3 last night. The ROM was pretty functional, but still has some problems. Around noon today, I flashed back to what I was using before CM10.
GoogleNow was working with voice. No problems there.
Camera worked a couple times, and failed a few times. Once it fails, seems like you have to reboot.
The UI isn't exactly running smoothly. Scrolling through homescreens is fine, but adding widgets to a screen can cause stuttering. A little lag shows up now and again. From the CM10 logs, seems like they haven't fully optimized the Butter code for the S3 yet.
Battery life was awful. This could be any number of things at the moment.
MMS is hit or miss. I could send, but couldn't download. MMS doesn't work with the stock messaging app, but Handcent could send them without being able to receive. Didn't try GoSMS or any others.
The phone ran hot. After installing, I restored some apps with Titanium. The phone was much hotter than it had ever been before. Not scalding hot, but noticeably warmer. Not sure why that's happening.
Notifications worked great.
It's coming along, but not a daily driver yet. This was a 7/20 build that I installed. I would assume other carrier models of the GS3 have some or all of the problems listed above, but I'm not real sure.