I know I've seen this discussed before and I believe the only difference is the cooling fins. It seems to me the full size has them on the back and the Beaumont radio has them on the side.
Hopefully our member 68SD396RAG will see this and post. I'm sure he knows the details on it.
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1966 Strato Chief 2 door, 427 4 speed, 45,000 original miles
1966 Grande Parisienne, 396 1 of 23 factory air cars (now converted to a "factory" 4 speed)
The shaft length (for volume and tuning knobs) may be different as well. I know I've run into this type of question before. You may find the radio fits, but the shafts stick out too far (or not far enough) and look funny.
I think the only problem that I have run into with big car radios in a 68 are the fins location on the big car radio are on the side rather than the back of the radio.The fins coming off the side on a radio from a big car AM./FM will interfere with the heater controls on an A-body.I have both so I will take a look again to double check it all.I have one in my wagon which I know was from an A-body.I think the fins can be moved though if I am not mistaken.