I had the same issue, I upgraded from 4S to S3, on the same day I upgraded my Macbook Air to Mountain Lion.
OSx will not mount the S3 because of the file system on the phone is different, so you cant sync this way.
But samsung have made an app to solve this. Its called Easy Phone Sync. Its in the Google play store. You also need to download the app for mac from the easyphonesync website (google it)
Run it on your phone, then on the Mac, and it mounts the phone, and syncs Itunes. It will even copy pics & contacts from your Iphone back up storted on the mac.
Only limitation, it will not copy DRM protected tracks & video to your phone. But itunes songs are now DRM free.
I did all this last night, worked a treat. Hope it helps.