The REAL difference is that you can find parts for a '34 Ford. Try finding anything for a '34 Plymouth.
Not telling me anything new.

Whereas, there are thousands of sources for Ford parts, there are a handful for Mopar parts. Ply-do out of Delbarton WVA is one of the larger suppliers of NOS and repro parts for early Mopars.

As to some of the differences, the bodies for the Mopar's, Fords and Chevys are similar, with the exception of the shape of the rear window and the grill and front valance shape. Mopar's hoods were longer, but wheel base was the same or less than the Fords. The Plymouth PC model was 108" wheel base and the PD was 112. The Ford was 112. Fords had a V8 option, while all Plymouth's were all straight 6's. Body widths was similiar but I don't have exact measurements. In 1933, both Ford and Plymouth had suicide doors.

Not sure about 33 Plymouths, but 34 Plymouths also had a steel strengthened body (Chevys used wood), a partially boxed frame and an independent front suspension (IFS), something the Ford wouldn't have for another 12 -13 years. Mopars also but their body serial numbers on a plate attached to the passenger side B pillar (door frame).

Actually I have found that some small Ford interior parts, like door handles, will work on Plymouths.