The culprit is "Cell standby," which on an unmodified GS3, appears to be a regular power glutton. But what's actually going on is that the phone's framework-res.apk appears to contain an incorrect value for how that power consumption is calumniated. Its base value of 34mA is more than ten times higher than expected (up from 2mA on the GS2), leading to the phone showing more power being used on it than is actually true.
There's a fix that modifies the value from 34mA down to 3.4mA. While it's not a perfect solution -- relying on guesswork -- at least it makes the phone report power consumption that's in the correct range.
We've yet to hear any response from Samsung regarding these findings or if there are any plans to correct the value in a future update.