A center-tapped is just a single winding with a tap in the middle. It gives you no option how you can use it.
OTOH, a dual winding with the proper two wires connected together performs exactly the same as a center-tapped winding. BUT it also gives you the option of connecting the windings in parallel for "half" the voltage, but double the current.
Disclaimer: This applies to "ordinary" cases at low frequencies (power mains, audio, etc.) When you start getting into esoteric applications, RF, etc. it is a different discussion where stray capacitance starts to have an effect.
Replacing a center-tapped transformer with a dual winding transformer of equivalent voltage and current should be a slam-dunk. Don't over-think it.