Battery Elimination Circuit Powering Flight Controller
If your flight controller already have its own DC/DC converter you should go for it, because it is probably designed for this particular use. 

Most speed controllers with BEC are based on linear regulators. Basically these regulators turn excess voltage into heat, the more current you will draw the hotter they will be. If, for some reason, they become too hot they will go into protection mode, and stop to work. 

To disable a speed controller BEC just disconnect the red wire from the from servo plug, unless your flight controller board already have a system allowing to choose the power source.