I have never noticed this.

Here's my 2 cents...

I think they move in unison, but possibly at different speeds. If I were an escalator engineer I would design it so that the same motor powered both the stairs and the handrail (seems logical...right?). The hand rails probably have a longer track to travel (since they are higher than the steps), so assuming the handrails and the stairs move in unison, but the handrails have a longer distance to travel wouldn't the handrails actually be moving faster? (distance/time=speed)?

Where are these escalators that you speak of?