As an NU undergrad I loved both the Stuffed and the Pan (Naked and the Dead; The Wound and the Bow, The Nice and the Good, The Fox and the Hedgehog, all the great dualities of the humanities).
At that time, (late 70s) Carmen's had the rep. (accurate or not, I have no idea) of making the pies in house, while Giordano's was reputed to distribute them from some central location.'
We also loved the Howard St. Edwardo's, though even then there came a point where I found the crust to white-bready and not vigorous enough to hold its own with the rest of the pie.
We also liked Gulliver's a lot.
Though Malnotti's was around, I never got to know it.
Once Carmen's began to expand, we found we didn't like it so much.
I don't think I've had a stuffed pizza in decades. Not an idealogical choice, just a gradual evolution.
Our local (Hyde Park) Edwardo's produces pretty mediocre thin crust (which our son is addicted to), and I haven't bothered to try their pan/stuffed.
As far as the dizzying ambiguities of taxonomy go, I had always understood "stuffed" to mean a double crust with sauce on the very top, while "deep dish" and "pan" signified the same or similar pies with a thick bottom crust (with or without cornmeal) made in an actual pan and then, ideally, de-panned (trepanned? No.) tableside.
Alone among my circle, my favorite pan was always the orig. Gino's East with the cornmeal as well as coarsely chopped tomatoes on top rather than a smoothly pureed sauce.
"Strange how potent cheap music is."