LTE coverage map is a marketing win for VZW but is substantively less significant.
1) IIRC, Verizon has somewhat slower LTE. I can't remember what the difference is. Possibly due to load.
2) AT&T has much faster 3G and "4G" (HSPA+) than VZW's 3G.
3) AT&T's rollout of 4G is similar to their 3G and HSPA+ rollout - by and large, high-density populations first, and then descending to less dense areas. They were stupid by starting the rollout a full 2 years after VZW, but their rollout is slowly catching up.
Ultimately, if you're mainly in a big city or go to bigger cities, AT&T should be fine. If you go to a place with no LTE coverage by either team, AT&T is better because the 3G/HSPA ("4G") is faster. The key place where VZW has the advantage is the mid-sized cities (Spokane, Fargo, Buffalo, etc).