If the rider is in the exact same position, and using the same tires, and the same wheels, then performance will be nearly identical.
Hence we have Cancellara on the Domane in pro events, and a few others on endurance bikes in road races (including Sastre and Zabriskie).
The only way it'd make a real difference is if you can't get into a low enough position on the endurance bike.
Otherwise, I find the idea that a few cm of head tube generates a measurable increase in drag to be mildly amusing.