I have found the battery life to be pretty decent on the GNex. I have the extended battery, but if I keep a close eye on what is running, syncing, and make sure the screen is off when I am not using it, I can get 2 days out of a charge. I haven't used the GSIII or EVO LTE, but from what I've seen, the battery life falls just short of them, but still whips the tar out of the E4GT, EVO 3D etc, and flat out embarrasses the OG EVO. Everyone keeps saying the radios stink, maybe it is because I switched to Verizon, but I have not had a problem with signal.
Maybe I need to go try out a GSIII, but I just don't understand why everyone is ripping the GNex. It is really great looking, the development community is robust, the stock software is awesome, oh yeah and it's also a smartphone.