A320 cabin is definitely wider, especially at the back. I remember one flight in the rear row of seats on a B737 which were all occupied, we couldn't all sit back at the same time as our shoulders overlapped.
The flightdeck is noticeably bigger as well, the jump seat can slide behind the F/O and there is standing room behind the Captain. No stringing up a deckchair in the doorway.
Baggage containers instead of hand loading should speeding upon the turn around times.