Unstable 11-13.8 volts to 12v regulator. DC-DC buck or Zener diode, how to do it better?
As you do not put a schematic diagram I think you have an external board that you have no control over. In view of this it makes sense to add a Buck converter, since it allows you to control the regulation of output voltage and have a high efficiency. The voltage regulator (zener) can do it, but it is not completely efficient.
The only detail you will have is that when you add the Buck converter it is possible that you introduce noise to the board since it may not contemplate its inclusion.
But since the application is charging a battery, this may not affect the PCB you use.