Center tap transformer with full bridge rectifier, number of rectifiers
If you want to do approach #2, you need two fully isolated windings. The way you show it has two diode drops in one direction shorting out the windings as @WhatRoughBeast points out. You cannot use a center-tapped winding- the common must be made on the other side of the bridge rectifiers.  



The advantage of the second method (with two secondary windings isolated from each other) is that it uses the transformer more efficiently if the loads on the positive and negative rails are greatly imbalanced. You can get as much as 24% more DC current out of the transformer by using the two bridges.