Full wave rectifier vs full wave bridge rectifier
The CT rectifier has half the number diodes and has half of the diode conduction losses. But the secondary utilisation factor of the transformer is not as good because each half of the secondary conducts in half-wave pulses. This means that the transformer is larger for the CT rectifier to do the same job with the same transformer secondary copper losses.
The CT rectifier is still used today when the output voltage is low and diode losses therefore are a significant percentage of the output volts. On a SMPS the transformer size penalty is not so bad because the transformer is so much smaller anyway. The CT rectifier makes it easy to get all the diodes on a common heatsink which is a definite production advantage. The CT rectifier has twice the peak diode voltage for a given DC output voltage. This can be an issue because silicon Schottkys are difficult to find above 200V.
If you intend to place MOSFETs across the diodes to reduce voltage drops even more you get twice the peak volts as stated before which can mean more Rds(on) for the FETs but the bridge has two FET Rds(on) drops. The CT rectifier is easier to arrange the gate drive. So all of this really has to be taken on a case by case basis. You cannot say that one is better than the other.
The top schematic is a double half-wave rectifier alternately taking half-wave power from the top and bottom halves of the transformer. This configuration has the advantage that there is only one diode in circuit at any time and so losses and heating are reduced. This configuration was also suited to valve / tube rectifiers.
Figure 1. Full-wave valve rectifier, looking sad because she's been replaced by semiconductor diodes. Source: Wikipedia.
The transformer on first glance looks more expensive as the secondary winding is doubled. The average current, however, is halved in each side so the wire gauge can be reduced.
The main differences are that the two-diode circuit requires a center tapped secondary, but has only one diode-drop in series with the voltage.
Silicon or Schottky diodes are cheap and small, so the number of diodes by itself is usually not the issue. Sometimes AC comes at you other than thru a transformer of your choosing. In that case, you don't get a nice center tapped secondary. Also note that the center tapped secondary is more costly since only half of it is used at a time. The four-diode circuit can get the same (minus one extra diode drop) full wave rectified voltage from just half of the same center tapped secondary. This usually outweighs the cost of the extra two diodes.
If you want a bipolar (both + and - supplies with common ground), then it takes a center tapped secondary and four diodes.