So I just swtiched from an iPhone 4 on AT&T to an iPhone 5 on Verizon. With the 4, I had full 3G coverage in my office. Now, on Verizon with the 5, I get extremely poor signal indoors. Once I get outside, LTE comes right on, full strength (I sit 5 feet from a window, as well). This never was an issue with the 4 at all. I have tried turning LTE off and everything.
BUT, here is the kicker: If I turn off my phone, and turn it back on, I have LTE for a few minutes, at full strength. It actually works perfectly until I use the phone for more than a few minutes, or if I pick it up. If I leave the phone sitting on my desk, it stays connected to LTE. Once I pick it up and start using it for about 5 minutes, I go back to having no reception at all.