ASTM F 2282 is the standard that defines the requirements for Cold Heading vs. Recessed Head wire.  Recessed Head wire is a further subset of Cold Heading wire, so by definition it should have better workability, meaning it can be upset to a greater diameter or extruded a greater amount without the formation of cracks.  The following is an excerpt from ASTM F 2282:

Recessed Head Wire is employed when screw heads incorporate a recess configuration such as a crossed or
square recess. This wire involves more exacting precautions and controls than Cold Heading wire, such as improved surface quality and special wire processing. Exacting precautions and controls are necessary in the selection and internal soundness of the steel and in the preparation of billets for surface quality.

Special attention to rod rolling and to inspection of the rods is essential. In order to provide wire that will be soft enough to withstand the very severe cold forming operations, wire for all types of recess head screws is generally spheroidize annealed in process or spheroidize annealed at finished size, with the final drawing incorporated into the heading operation by drawing in process in tandem with that operation. When spheroidize annealed at finish size wire is so employed, the fastener producer should ensure that the final reduction is not
excessive.