Efficiency of a centre tap full wave rectifier(qualitative analysis)
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.