True you're breathing faster and your pulse is higher in order to use extra oxygen, but you're getting from A to B faster, so you have traded time for energy. I'm sure it's not exactly the same, but I believe as in my earlier post, it's about the same.
It depends also on efficiency of the individual body. If your peak efficiency is at a run, then you'll happen to move your mass the same distance as the other person who's peak efficiency is at a walk, much faster. But I still would want to see a table that shows all the factors before saying either side is more accurate. It's a fundamental rule of physics that it takes a certain amount of energy to move a certain mass, a certain distance with certain resistance.
Charles