I have one of the few GNex's that has had very few problems. It is rooted and running custom ROMs, but I don't often switch ROMs so it isn't a huge deal. It has been the best Android phone I have ever owned to date.....and I have owned MANY. (OG Droid, Incredible, Charge, GNex). I would switch to the GSIII for 3 things....1. Better battery life. 2. Better screen outdoors. 3. Better signal strength (my wife's IPhone kills the GNex in signal strength).
I have seen the poll of GNex users that have switched to the GSIII, but not many are talking specifics.
Can any former GNex users tell me how much better the batter life is and how the screen is outdoors compared to a GNex? I have the extended battery in my GNex and with a little above average use, I barely can get a day out of it.