Perhaps your mention of "depth" is what confused me. Disney used several layers of artwork moving at different speeds. Filmmation may have used only 2, foreground cell animations and a background.
For me, it's almost intangible, but watching films on blu-ray gives me an added sense of depth that I don't get from SD formats. I don't know if it's the added detail or what it is, but some films where this was especially noticeable to me are Casablanca and Patton.