They have both. Like many pizza joints, they have a list of specialty pies, but also allow you to customize with anything you like. I believe there is also a specialty 4-cheese pizza.
We really enjoyed Via Napoli when we went before the Princess 1/2 marathon. We met some friends who had been before and suggested it. I wasn't sure because we've always avoided Italy as we have good, fresh Italian back home. We ended up loving it and have made an ADR for our upcoming trip. We are fans of thin crust pizza and this is certainly good, but it is more like the pizza you get in Italy rather than Americanized pizza.
We are from Arizona (home of Pizzeria Bianco, named more than once as a top 10 pizza places in the US) and central Illinois, both regions where thin crust pizza cut into squares is more common than Chicago style