Hey man..............remember you from the infamous VZW Galaxy Nexus thread. I personally had no luck at all with that phone, be it VZW or GSM. BIG disappointment, to me at least.
I also am looking at either of these 2 phones. Leaning toward the Note III because I think it may get more dev support...........who knows. I currently have the S3 on AT&T and love the thing. Time to move on however to something better/different. The current S4 was just not that big of an upgrade so I am waiting. Might wait for the stats on the Nexus 5 also?
Take care and enjoy whatever you decide to buy