Numerous independent speed studies show that AT&T consistently has faster data throughput than Verizon. Not true for telephone service though, but no one cares about that on an iPad. All that said, it really comes down to where you want to use the iPad. For my money, and it is my money, I travel a lot and have had consistently good service with AT&T. Not many cities offer 4G/LTE for any service but new ones are being added every day.
Your choice of service for the iPad is unrelated to who you use for telephone service, totally separate contract.