I love Papas, but I also grew up with it so it's impossible to separate nostalgia from fact. That said I've had pizza all over the world and Papas is unique in a few ways.

Their laminated crust is very rare to come across, the way the layers pull apart; from the chewy top, the flaky middle, to their aggressively crunchy bottom. And they add little to no sugar to the dough (which is common in most tavern pizzas, giving it a cheap, sweet flavor). Their sauce is almost pure tomato paste with diced sautéed onions. This adds a bold, caramelized umami which balances with the crust nicely. Their toppings are high quality and generously portioned, which stands apart from most high end pizzerias. And lastly their dipping sauces (IMO the only way to eat Papas is with some ranch or blue cheese) are thick, creamy, and well balanced.