For no other reason than that I feel like it, here's the New Orleanian review of Connie's and Lou Malnati's (did not try Giordano's, mainly because they don't have any pictures of their pies online, and did not try Gino's East, primarily because, despite the appetizing appearance, they end up being like fifty bucks a pie shipped---a little too pricey for me compared with about $30 each, shipped, from Connie's and Lou Malnati's.)
Crust:
Hands down, Lou Malnati's. Tasty, crunchy on the edges, soaks up some sauce giving it a nice tomato-ey taste and texture on the parts in contact with sauce, just all around excellent, especially compared with the rather pedestrian and doughy consistency of Connie's.
Sauce:
Both good, with a slight edge to Lou Malnati's for texture and the way it kind of seeped into the crust in the cooking process. Neither caused heartburn, which is an issue I've begun to have with pizza and pasta sauces as I get older.
Cheese:
Again, both good, but, again, an edge to Lou Malnati's, larger than the sauce edge. Lou's cheese is perfect in proportion, and melted evenly in the cooking, while Connie's cheese was in chunk form on the pizza, and melted and cooked somewhat unevenly. Not bad, mind you, but I gotta take points off for the uneven melting cause by the chunks of cheese.
Sausage: (I am not a pepperoni fan, and ordered sausage pizzas from both for my eating.)
Hands down, Connie's wins this one. I don't know the details of their ingredient sourcing, but Connie's sausage was flat out better and more flavorful than Lou Malnati's. Though I must admit, I am not entirely sure if I perceived this because of actual quality, or because the sausage in the Connie's pie was in large chunk form like their cheese, but there it is.
Customer service:
Both shipped promptly, so I have no negatives for Lou Malnati's, but I must give extra points to Connie's, given that they flat out state that they offer no refunds or returns, but they did volunteer to send me two replacement pies free of charge after their first two showed up on my front porch packaged as if for local delivery in Chicago, just with a larger shipping box. (They were quite smelly when I encountered them.)
Overall winner:
Sorry Connie's, and I will in future buy a couple from them, just to make sure to reward good customer service, but barring said one order from Connie's, I am confident that every time I crave pizza for my once a week cheat meal, it will be a pizza from Lou Malnati's. Like the one I am sliding in the oven in about five minutes or so, when the temp hits 425 in there.