Transformer efficiency is considerably worse in a full-wave center tapped rectifier. Since each winding only conducts a half cycle, the copper losses in the secondary will be twice as high (I^2*R: if you conduct twice as hard for half as long, the losses are twice as high). Generally, copper losses are more significant than diode losses, so double the former to halve the latter is a bad deal except at low voltage.
Schottky diodes are a good solution, but watch out. Some (mostly lower current) rated schottky diodes have high forward drops at maximum current. Their reverse leakage can be also problem especially at higher voltages -- make sure to check the leakage at the expected operating temperature (including the temperature rise from the forward conduction). They also create unnecessarily fast switching transients in low frequency rectification applications that can increase noise. None of these problems is particularly serious, just make sure to check the ratings before you drop them in your circuit.
Personally, since you are talking about 50 V, I would just eat the second diode drop using standard high current silicon diodes. It is a drop in the bucket as far as efficiency of a line transformer linear power supply.