LDO to Power ESP-12F
If you supply the entire circuit board with a 3V AC/DC supply, it makes no sens to replace the 3V supply for a 5V supply + 3V LDO. 

However if other components on this board use 5V, then you must provide 3V to the components which don't support a higher voltage. Then use a LDO.

A LDO is a voltage regulator. There are LDO and non-LDO regulators. LDO only means that the voltage difference between the source and the desired output can be very small while non-LDO means this difference must be at least 2V. If you apply 4V on a non-LDO regulator, you won't have 3V at the output and probably nothing at all. It must be higher than 5V. Usually they work with 5V but there is no guarantee.
On a LDO you will have 3V even if you apply 3.2V.