First off, tell us who the famous person is?
I'd have the CLA done to the camera you want to use. Take each one, run thru shooting with each, ignore the shutter for now. Do your lenses focus smoothly on both? How is the rangefinder spot? I've had a number of IIIf and IIIc cameras over the years and have always held on to the ones with the best focus patch, as some of them were so faint I couldn't focus. What condition is the rest of each camera in. Take up spool, good condition? Bottom plate, good condition? How much brassing and finish marks are on each? What condition is the vulcanite?
Again, after going thru all this, I'd have the CLA done to the camera you like using the most.