I would suspect Fast. Its covers more than twice the distance for a given amount of time as does Medium (15 m/s vs. 7 m/s) and, while the battery may not last quite as long, Medium isn't going to provide twice the flight time.
You have to be going at least fast enough to give the rotors clean air to bite into. If they're dealing with the turbulent air beneath the rotors, they have to work harder to maintain altitude. Beyond that, there's probably a point of diminishing returns and it's likely to be something short of full power.
I dunno. Take a few batteries into the field and fly some straight line courses and tell us what you find.
I recommend that you fly upwind to a specific point, then return home. This way if your battery poops out you are at least returning downwind to home. When the copter is home, note the battery remaining. The repeat at a different speed.
Your results may answer a question I've had for a while. Do the counter-rotating props on a quad contribute to the transitional lift like a conventional helicopter? In a conventional helicopter there is a point when the forward motion results in additional lift, reducing the horsepower needed to stay aloft. In other words, a helicopter hovering burns a lot more fuel than one in forward flight. If the quad rotors contribute lift in forward motion then faster should be more fuel (battery) efficient.
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