In a centre tap full wave rectifier the output voltage is half of the input(secondary coils voltage) voltage, so the power is half of power of secondary. Also in half wave rectifier the only half of the cycle is rectified but the voltage amplitude is full so the power is half of power of secondary coil. Thus I conclude that the efficiency of both half wave and full wave rectifiers are same since both of them deliver almost same power per cycle. Is my reasoning and conclusion correct?
Start with a half wave set up with a transformer of certain primary and secondary windings. Both the primary and secondary sit idle for every other half of the cycle.
Take the same transformer, double up the secondary winding and use full wave rectifier. The two secondary windings still sit idle for every other half of the cylce while working alternately. The primary winding now works both halves of the cycle. When comparing to the first transformer, this transformer has twice the copper for the secondary, it may use the same amount of copper for the primary, the peak flux remains the same, the transformer size probably need to increase due to added copper for the secondary and the heat dissipation increase, and you can get approximately twice the power output for twice the power input.
It seems like the answer to your question depends on your definition of efficiency and what are being held constant.
