I think the answer is pretty easy but only because the two drills are not even close to comparable. The corded drill will consume a lot more power, even if lightly loaded, because it is a much more powerful drill. Loading it lightly will not make it come as little power as a cordless drill. To prove it you would need to measure consumption but I am pretty darn sure this is the case.
For comparable sized drills, the cordless will consume more because of the ineffiency of converting the AC to DC. Differences in designs of motors is an even smaller factor.
But big drills consume more electricity than little drills.