Which fleet would gain most from an early CIC

Who would benefit most from receiving an early combat information center?

Probably the British, although the supporting communications, sensors, and operating practices matter as much as the center itself.

An early combat information center would most help a fleet that coordinates many moving units instead of operating in monolithic blocks. That favors the Royal Navy. The room itself could only achieve so much without the communications and technology needed to operate it. Better systems could have helped the Americans at Midway, while Togo is considered a commander who could have exploited modern sensors and a CIC at Tsushima.