Most areas differ, and drastically so with SPrint and T-Mobile. Here's how my area shakes out:
Verizon - The most coverage, network is loaded but not overloaded, speeds are decent. Unfortunately, there's a few spots with no coverage, and said spots include my home and my office.
AT&T - Almost as much coverage as Verizon, and they cover the spots Verizon missed, but per SOP for them, their network is way oversubscribed. I doubt "VoLTE HD Voice" will last long in their everlasting quest to squeeze more users into less bandwidth, but their customers seem to be used to it.
T-Mobile - Still EDGE in some places, but being converted to LTE. Very good HSPA+ coverage. Lightly-loaded network comparatively, speeds are fast and calls are clear. Widely available WiFi calling dovetails well with widely available Optimium WiFi service from the region's cable company.
Sprint - Still EVDO in the entire county, LTE being deployed to the south, turns into Spark as you get closer to NYC, but they seem to have halted LTE short of my county. The EVDO coverage is not terrible, but it's all PCS, and is patchier than T-Mobile AWS coverage.
This is not definitive of course, other areas will be VERY different, a lot depends on local population densities, terrain, local spectrum holdings, and even zoning laws (where are you actually allowed to build a tower). I will say that compared to the other carriers I'm the least impressed with AT&T and Sprint's overall business decisions, particularly investing so much in spectrum licenses way over 2 GHz (as in countrywide REA-size licenses) that have both range and penetration issues. That's my own personal opinion though, I know some others are completely in love with BRS.