Michael Parrish asked:

"Is there any functional difference between the round and flat leg style 
calipers?"

The screw thread of the round-leg ones is finer than that of the Fay and Yankee.
It makes them distinctly slower in use. That's why I prefer the Fay (the square-
legged ones where the screw goes through the leg). I don't need the extra
precision of the finer screw.

Tom Conroy