For about 2 weeks now, I have noticed terrible LTE connections and overall poor data service. Right now, I'm looking at my Galaxy Nexus with 2 bars of 3g. If I'm outside, I'm lucky to get 2 bars of 4g. Inside, I don't even try. Zero penetration indoors. I live downtown and work in East Memphis and it's the same all over the city.
What's worse is that I have a AT&T Blackberry and AT&T WP8 (both company issued for app testing) and they stay 3+ bars of LTE. I now do most of my browsing/social media on either of those phones. When my contract is up, I will definitely be considering switching back. I switched away from AT&T a few years ago because Verizon just had better coverage. Seems like that is changing now.