Yes, the international SGS3 is different than the AT&T one I have, but I would advise you to stay away from CM9 and definitely CM10 for now.

At least on the US versions that use Qualcomm chips, many drivers are broken or barely working. Wi-Fi, camera, and bluetooth in particular. I will expand on this in a moment, but I just want to post this before you do something you may regret...

EDIT: More info

I've had the SGH-I747 (AT&T) SGS3 for a couple weeks. I flashed CM10 to it within a couple hours of purchasing. It was so insanely buggy, that I then flashed CM9. CM9 wasn't in a much better state, but it was usable in a very basic sense. Bluetooth was broken, wifi was buggy, and the camera would crash, but it could make calls and not need random reboots.

Right now, I'm on CM10 again and I'm using it as my daily driver. There are some big bugs, however. Apple access points will crash the WiFi. Other access point may crash the WiFi. The only access point that definitely works is DD-WRT on my Linksys E3000. When I'm at work, I have to turn off Wi-Fi since we use Apple AEBS as access points.

Bluetooth is actually working to some degree now. A2DP and hands-free calling seem to work for me, but a lot of people are complaining still. If you need to use a bluetooth headset, I would stay away from Cyanogenmod at this time.

The camera driver still crashes if you refocus too many times before snapping a photo. The camera won't work again until you reboot the phone.

Early CM10 ROMs were plagued by "black screen of death" issues. The phone wouldn't wake from sleep. The only remedy was to pull the battery or hold Vol +, Vol -, and Power for 20 seconds to force a reboot. This has happened to me once on the most recent release, so it's still not totally fixed yet.

There is an issue with some phones losing their IMEI if flashed improperly. The cause isn't really known the last time I checked. I believe this is limited to Qualcomm-based phones (LTE models).

I still have a problem with the phone sleeping too deeply when on cellular data only (no active wifi). Notifications don't come in after the screen has been off for some amount of time. This seems to just be down to the ROM being immature and not having proper power settings worked out.

Other than that, I have been happily living with the phone for 2 weeks now. Things are getting better, but I would just stay away from AOSP-based ROMs for now. It's just too new.