Current calculation in Capacitor drop supply?
The only advantage of having zener before the rectification diode is less component count..!

Output voltage is the function of choice  of the zener and any voltage dropping elements e.g. the diode as in the top circuit.

In this types of circuit the continuous current limitation is always dictated by the input Xc and nothing else, but peak momentary output current is determined by the final output capacitor.

For example if you use 1000uF low ESR capacitor for the output, you may able to draw even 100 Ampere at 5Volt for a brief 1 millisecond.