More like at my friend's house and when I drove to a town just north of me where they have 4g as well as at my local verizon store. Here are the results of my testing with different phones.
At my friend's house, in full 4g coverage. 3g got 2-3 bars on the gnex, so -83 to -93dbm, it is much more inaccurate thanks to verizon's update from what I understand things used to be reported better. I get 1-2 bars of 4g, but the signal is about the correct amount weaker given that 4g uses rsrp instead of rssi to estimate signal. However I find my phone has trouble getting 5mbps down. Actually i had 2 galaxy nexuses at his house, one could just hit 4 down and 1.5 up, the other one which i kept gets maybe 4-8 down and 1-2 up, but it is clearly struggling just to hit the 5/2 minimum verizon advertises even though 4g signal is not weak, and verizon's network should not be overloaded.
Separate from this, I went to my local verizon store and tested lte there. There is no lte in the area, but the store is on a hill and so phones pick it up. I got my galaxy nexus to get lte for just 1 speed test, it then dropped, speeds were fine oddly enough, I got something like 6 down and maybe 1.5mbps up, once again upload can't hit good speeds on weak signal. Going in the store, the motorola razr's found 4g fine and reported a stronger signal, and got 10-12mbps down and also 1.5-2 up, so same upload issues. The galaxy s3 barely found 4g, and couldn't hold it. The galaxy nexuses and mine in the store were unable to find it, and I couldn't find it outside of the store again. Clearly on fringe areas where coverage isn't quite reaching yet, the motorola phones pick it up and that's awesome. The samsung phones don't.
Furthermore I went to the town just north of me where there is 4g, and drove to a spot where my phone had sort of weak 4g, but that was before I knew about rsrp. I was getting about -105 to -114 dbm on the galaxy nexus and it struggled to hit 4mbps down as usual, despite the fact that this signal would be about equivalent to getting -83 to -93dbm on 3g. I then tested on my samsung stratosphere. I do not know how strong the signal was, but it clearly found 4g just fine and got 10-12mbps down super easy and got the same on upload while the 2 galaxy nexii were lucky to get 2-3mbps up. This showed me that once again the galaxy nexus struggles in signal that is even semi weak, even if such a signal should be healthy.
I don't think you can even blame the via chip, because my stratosphere has the same via chip, just one model number lower. Overall I think it really is just that the galaxy nexus has major issues. I don't know if a motorola phone would solve these with stronger signal, I also don't know if an s3 would not have these issues just because it works better with weak signal. However I do know the galaxy nexus has issues in places where it should have no issues, and where even other samsung phones have no issues.