All else being as equal as possible.... (not very possible) the brushless would draw marginally less power.
But (in model size motors) the brushless motors all use rare earth magnets which are more powerful than the magnets used in all except a very few brushed motors. The stronger magnets make the motors more efficient and thus you get more useful power for the same watts input.
There's also the better efficiency of the brushless ESCs helping the brushless power systems be more efficient.
So we generally see a significant improvement in efficiency with brushless.