This is my 2nd phone on VZW; my first was the X2. The X2 was nice, but never really felt right to me; IMO. The Galaxy Nexus for me is great, and I'm really loving what Google did with ICS. It feels polished, and it is very smooth and does what I expect when I expect it. I've only experienced a couple random re-boots and have had to do zero battery pulls.
Battery life could be better (and yes I have an extended battery)... but I spent $20 for another charger that I could leave at my desk as the USB cable on my laptop took forever to charge the phone. Data movement to/from the phone is pretty quick and I love being able to use everything on the phone when it's attached to a PC.
I'm using Dolphin for my browser, but I've come to like that browser best (stock was nice though). I use PowerAMP for music, and it works extremely well. I don't have any of the music skips I experienced on the X2.
I had to add a case as I always felt like the phone was going to slip from my hands (I was getting paranoid, lol). I have the extended battery, and found that the Incipio VZW sells fit ok. Slight bubble, but not really noticeable. I found that between the slight weight added with the extended battery and grip ff the case the phone feels very solid and natural in my hand. Portrait or landscape feels natural and not lumpy like the X2 did.
I've never rooted a phone, though I've had quite a few android phones. I am really liking getting away from skins (I've used Sense and Blur) and using the phone in its native form; maybe I will root this one and try some roms down the road.
4G is great, and super fast. I leave the phone on 3G most of the time and just switch over to 4G when I need it; kind of a pain, but it saves battery some. I also turned off NFC and that helped with battery life some.
We have seen a lot of "replaced my Nexus with..." threads and a lot of Nexus bashing. I'm sorry others aren't enjoying this phone, but there are some of us that really are; despite some growing pains the phone has, but I expected that being a new phone and new OS. I just wanted to chime in as an average user, and one who has been with Android from the days of the G1.
As an aside, I'm pretty happy with VZW after coming from T-Mobile too. Costs a bit more, but the coverage is outstanding; customer service via phone has been stellar (stores are hit and miss).