Coming from a Motorola X, I've had my 16GB GSIII for 3 days now. Absolutely love the phone so far. I've had just as good battery life as my X. I have not experienced any radio issues. I am personally getting better reception than I did with my Motorola X - no dropped calls, strong reception, and no delay with receiving messages.
I did experience some issues on the first day with downloading the same apps I had on my old X. Clearing the cache and data followed with a reboot fixed that. No other issues to report since.
Compared to my fathers Razr Maxx, the GSIII is getting just as good reception. I don't understand why everyone is complaining about the reception and dropping data. Anyone ever think it may just be Verizon? Wifi fixes that problem.