The advantage goes to the F4 in this scenario but anything can happen in a dogfight and it only takes a simple mistake such as an overshoot to reverse such a situation into the other pilots advantage. So speculating on the outcome is a waste of time but as far as performance goes the F4 is quite awesome and the missiles may/may not work but having the gun there is a big advantage.

Heres some examples of real F4 dogfights: