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If you doubt that answer, slip over to rockauto.com and enter the specifics for each, you will find pictures of the available steering gear.
Once you look at the images of each, you should get the idea, that there is an easier box to interchange. Horizontal vs vertical pitman shaft, for starters.
What is the difference between a steering gear box for a 1964 Ranchero compared to a 1964 F-100?
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Falcon steering gear will not work on F100/350 and vice versa.
1961/64 F100/350 steering gear box: The steering shaft goes directly into the gearbox, so you have to remove the steering column and gearbox as a unit and take it all apart to replace what is needed.
Beginning in 1965 F100/250 2WD, 1967 F350: A steering coupler (aka rag joint) connects to the steering shaft then to the gearbox.
So once the coupler is unbolted, the gearbox can be removed leaving the steering shaft and column in place.