The first answer is that rectifiers are not regulators. Rectifiers make no attempt to regulate voltage.
The second answer is that a full wave rectifier will require half the capacitance to reduce voltage sag between power pulses, compared to a half wave rectifier.
Typically for a given value of reservoir capacitance full-wave rectifiers give better regulation than half-wave, because the ripple sag time is approximately halved.
A bridge (Graetz) rectifier however has two diodes in the path instead of one for the half-wave type, so the rectifier drop can be larger, although this is somewhat offset by the fact that only half the mean current passes through any one diode.