Some airports I know pretty well, and I know how far things are, and my options. Then I often just walk, because the exercise and stretching after / before a flight is good for me. Take Phoenix airport, or Oakland, or Reagan National for example.

Other airports, especially if it's kind of a new to me airport, I usually take the moving sideways and the escalators. I don't know how far I am going, and I usually really like the chance to look around, make sure I am going the right way, all while moving. First time in Sacramento Airport for example, or LAX.

I also seem to travel mostly to mid sized airports that don't really have alot of those options most of the time. Albuquerque, Oakland, Kansas City, etc. I don't think those places even have moving sidewalks.