Actually, the Chief of Starfleet Operations doesn't mean in charge of all Operations Branch Personnel. The title is extrapolated from the US Navy's highest ranking officer: Chief of Naval Operations. The CNO is in charge of providing the Navy's strategic direction and is the Navy's representative on the joint chiefs of staff.
We first heard the title of CSFO from Star Trek II, I believe. The implication was that Kirk was in charge of the strategic deployment and management of the fleet...more of a command function than a TNG-style operations function.
IMO, the CSFO would definitely wear red.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz