There's an old adage in the airline biz that flyers always hate the last carrier they flew. That seems to be true of cell phone carriers, as well.
The biggest single advantage of AT&T is their use of GSM technology which makes it possible to use virtually any of their devices (including the iPad) in Europe (and much of the rest of the world) by simply changing a SIM card. But if you don't travel outside the USA, that's a wash.
For years AT&T had a very bad reputation in NYC, San Francisco, and some other cities. That appears to have changed significantly in the last couple of years. If you're interested in more than anecdotal information, though, you might want to check a site like "RootMetrics" which rates coverage and performance based on thousands of samples of user data.
In terms of performance, 4G/LTE networks are far, far better than 3G. (On average download speeds are 8-10 times faster than 3G). And on that score Verizon is far better in terms of current coverage and actual performance than AT&T. AT&T is just beginning to roll out its 4G/LTE network; Verizon already covers almost 200 metro areas.
The problem is that you cannot access either Verizon's or AT&T's 4G network with a 3G iPad. To take advantage of 4G/LTE networks you have to purchase a mobile hotspot from one of the carriers and (likely) sign up for a two year contract (not month to month as the iPad coverage provides) at about $50 per month (for up to 5Gigs of downloads). You can then connect your iPad via wifi to the hotspot.
I travel a lot and have to connect my laptop as well as my iPad in areas where good wifi coverage is spotty. So for me the Verizon 4G/LTE hotspot is a good alternative. I recently took a week long trip to Kalamazoo, Michigan and used the Verizon hotspot. It was about 15 times faster than the "free" wifi in my hotel. And over the course of 7 days, I used almost 3Gigs of downloads. That trip alone would have run $40 on a 3G iPad and the performance would have been a fraction of what I got on the hotspot. Plus it covered both my iPad and my laptop.
Of course, if you don't plan to use the cell network much, ymmv.