I too have an AT&T iphone and have been debating switching to Verizon a bit after the iphone 5 rollout. For me it is a little more financial decision too, as my contract isn't up until next April, but my upgrade date for AT&T is the start of November. So if I switch to Verizon I'd probably take a $250 range ETF between two phones.
I had a very nice opportunity yesterday to borrow a coworkers Verizon 4G LTE phone (an LG model). For me it was a chance to drive around to areas I spend any significant time, compare signal strength, and run a quick speedtest. I learned a lot, and at this point believe I will stay with AT&T due to their significantly better 3G/HSPA+ setup.
-4G LTE is VERY fast - downloads between 20-30 Mbps. Areas it covered on Verizon were pretty extensive, Lansing MI for example I drove about 30 miles around the city (literally a circle) and have solid 4G the whole time.
-Verizon 3G is VERY slow - between major cities or more rural areas like where I live their 3G was a solid signal - but very slow compared to AT&T. Generally I averaged around 0.5 Mbps.
-AT&T 3G with the HSPA+ (I think of it like 3.5G) - most of the towers have the improved backhaul and deliver solid speeds fast enough for video. Some areas would download 3-5 Mbps, but some were as good ad 12 Mbps. It's not 4G LTE, but it is more then enough for my needs.
-AT&T Edge - I did spend a little time in 2G areas on AT&T where Verizon had 3G, but they are not areas I would spend much time. If someone were to be in a 2G area, they may be better with Verizon even with the slower 3G speeds. AT&T Edge download was around 0.1 Mbps. A bit confusing is one area (St Johns MI) on AT&T's map showed 4G (HSPA+), but while traveling there all I ever got was a full signal, but Edge data.
So for my needs I think I'll be better with AT&T for my travels around central Michigan. There is some solid 4G LTE coverage from Verizon, but the areas where they aren't yet are really bad for data. AT&T and Verizon have pretty similar 3G coverages, but AT&T has much better 3G speeds.
Three more factors - I'll save the ETF, AT&T customer services seems more generous with discounts (I'm currently enjoying $40 off for 3 months after inquiring about my ETF and discussing Verizon with them). Lastly - I'm a bit afraid that having 20-30Mbps service will lead to a bit better quality video, while using a lot more bandwith on video. There is almost a small comfort knowing my bandwith is enough for video, but not too much