The ability for helicopters to fight each other is more a function of weapons system design than maneuvering ability. At standoff ranges, high speed precision weapons are key and if you ever get into the merge a stabilized turreted gun with a lead computing and motion compensating fire control system would easily overcome higher turn rates or extension speeds.
MD did some interesting air-to-air work with the Apache 30MM system which never got into service. That gun is horrible for traditional air-to-air work because of the low speed of the round and rate of fire of the gun, but with a proper fire control system it was pretty effective against drone targets.
The Marine Corps proved the air-to-air capability of the Hellfire missile when they hit an F-18 with one during a gooned up non-autonomous laser designation shoot out in Yuma a few years back. The F-18 was lazing and the shooter geometry was backwards (shooting at the F-18). The missile saw the designating pod as the spot and took off one of the F-18's vertical fins.