I guess this response is too late for the orig poster, but in case someone else may find this helpful:
The only thing I don't like about the VZW GNex is the radio. I had come from the HTC Thunderbolt also and you can expect the GNex's radio performance to be noticeably not as good. I get about 15dB less signal strength (according to the About Phone -> Status) compared to the Thunderbolt. It's still usable, but sometimes I don't get a data signal or it's loss and I have to reacquire it (turn LTE off and on). According to VZW tech support, they are aware of this issue and are looking into a solution. But given the phone's age and that this is likely a hardware issue, I would be shocked if a software fix is ever released. However, as you can see from the earlier replies, this doesn't seem to affect all VZW GNexii, so you may not experience any issues.
I don't know enough about the S3 to compare them in that regard though. The S3, being also a Samsung, may have similar reception performance, or may be better (or worse?), I don't know.