Same issue here. Previously my wife and I both had the VZ Moto Razr running the Gingerbread OS. 3-4 bars almost everywhere. Once the Ice Scream Sandwich update came out, I updated both phones and immediately started having poor reception, dropped calls, data connectivity issues, and inability to send/receive text messages. I called VZ, they told me I could not revert back to the original OS and would send me out 2 phones with the Gingerbread OS instead. No more problems.
2 weeks ago, I purchased a Samsung Galaxy S3 from a friend and immediately start having the same issue again. I rooted and unlocked the phone and installed several different ROMS and radios but none solved the issue. I even got into a "dispute" with several XDA guys that "were not aware of any of the issues I was complaining about" and suggested that the phone was bad. I maintained my point that I "have" no issues until I use a phone that has ICS on it and that the problem lies within the OS, not the hardware. On another note, when I was with Sprint, I had the Samsung Epic Touch. I installed a ICS based custom ROM on it and had the same problems to. So just another bit of proof that the issue is with the OS and not the hardware.
Today, after trying all options, I will venture to the VZ store for a phone/sim. Even though I don't think this will solve the issues I'm experiencing, it will be the very "last" resort in this extremely frustrating journey.
I'll update everyone once I get back, though I'm not very hopeful.......