If you look at the national coverage of AT&T and Verizon, they geographic coverage will be nearly the same.
AT&T covers 300+ million people
http://www.att.com/gen/investor-relations?pid=5711
Verizon covers 98% of the population
http://www.verizon.com/about/sites/default/files/Verizon_Fact_Sheet.pdf
It is basically a statistical tie with each claiming to have the largest.
Both Sprint and T-Mobile have smaller network footprints.
Who has the fastest?
http://recode.net/2015/03/10/iphone-speed-test-att-tops-verizon/
http://www.fiercewireless.com/story/t-mobile-offers-fastest-average-lte-speeds-opensignal-report-finds/2015-03-12
Do a Google search and you can find all the carriers have won some sort of network performance measure (speed, reliability, % on LTE, dropped calls, etc.).
I would classify the difference between Verizon and AT&T as a Pepsi vs. Coke argument. On the major highways and cities (10,000 population and larger), the difference will hardly be noticeable. The difference will come in the rural areas or specific parks you frequent.
When someone says Verizon terrible (or great) or AT&T is terrible (or great)? It is worth asking why. I find people giving opinions about other carriers based on experiences that are several years old. Over the past couple of years, there has been a lot of network build out and consolidation. Just because they were driving in South Dakota 4 years ago and one carrier was great or the other poor, is not all that helpful. I also find people equating their device satisfaction with the network. If you are using an old hotspot without the latest network technology, don't blame the carrier. An iPhone 3GS is going to run slow on any carriers network.
Frankly, you will find that about 90% of the coverage will be the same between the AT&T and Verizon. The last 10% will be subject to your specific travels.
Your satisfaction with your wireless experience will be impacted by coverage but don't forgot about the other factors such as device/handset selection, customer service, network speed, network reliability, cost/rate plans, etc.
Personally, I have been a customer of Verizon, T-Mobile and AT&T over the years. All of them had pros/cons. Currently, I am satisfied AT&T customer. Here is what I like about AT&T:
-Overall, good coverage
-Fast LTE speeds
-US Based customer service centers
-Device selection
-Flexible rate plans
In your evaluation, look at your needs and priorities. Look at your frequent travel locations. All the carriers have coverage maps on their websites.