misconception of full wave and half wave filter rectifiers
Lets assume you have a center tapped transfomer winding as your supply. Lets say that the peak (not RMS) voltage between the two ends of the winding is V. I will also assume the diodes are ideal (zero volt drop when conducting)

With the full wave non-bridge rectifier you only use half the winding at a time. So your peak output voltage would be V/2 .

With a half wave rectifier there are two ways we can connect it. We can either connect it across the whole winding or half of the winding. If we connect it across the whole winding the peak output voltage will be V. If we connect it across half the winding the peak output voltage will be V/2.

An output capacitor will not change the peak voltage but it will reduce the rate at which the voltage drops away from the peak. How much it will reduce it will depend on the size of the capacitor compared to the current requirements of the load.

Since a full wave rectifier has peaks more often the output voltage with a given capacitor will drop less with a full wave rectifier than with a half wave rectifier.