I lived in Chicago for 15 years. Tavern-style pizza in Chicago can be good, but Piece's pizza (New Haven style) is better than most Chicago-style pizza. My go-to before I left the city was Crushed Pizzeria, which is Neapolitan-influenced. The only place I can ever remember eating decent tavern-style pizza is at dive bars. The thin crust from places like Giordano's and Rosati's is a soggy disgusting mess.
As you'd expect, since Giordanos and Rosatis are deep-dish spots. Malnatis will sell you a thin-crust pizza, too, and it's cut into squares --- but it's not Chicago neighborhood-style pizza.
