Wife had a Droid 1 and I have a Droid X. She upgraded to the Nexus. She gets 0 to 1 bars of signal on the 4G Network sitting next to me while I have 2 to 4 bars of signal at the same time. She is hitting spots out where she will get 0 signal.
This has been a big issue where some tech sites have done studies on it if you will.
Basically, the condensed version is that the Galaxy Nexus is reporting the correct LTE strength, whereas the Droid is reporting the EV-DO/1X signal strength.
Verizon said they will "fix" this in an upcoming update. Though I have noticed the same "problem" in the sense that my LTE drops out way earlier than it should.
I am also having signal issues. My nexus does not work in my house and gets very weak signal around the entire area where I live. My moto droid 1 worked great everywhere. Actually everybody that has verizon where I live their phones work great. I can't even make a phone call or text message, much less use data with my nexus. Verizon claims it might be a defective sim card and is sending me a new on.