Been to both, over-nighted in both. Volterra offers a museum and interesting Roman ruins. Cortona has a museum/fort at the top of the hill (although when we hiked up to see it, and the sign said it opened at 10, and we waited until 11 and no one came to open the door, we didn't see it!)
Either/or...they both have their charms
If you are traveling by train, note that the hill top town of Cortona is not where the train station leaves you - like Assisi, you will have to take a bus to the actual town, and that leaves you at the gate - parking lot area.
I vote for Volterra, it seems a bit bigger, and it's nice to walk just outside the city walls, plus the Roman ruins are wonderful to see, as is the Etruscan museum is worth a visit. The view from the wall is beautiful and I'm sure you'll have no trouble finding a nice family owned restaurant in which to have dinner.