here's a (not thee)difference: The roots of the stump stabilize the soil and allow for nitrogen fixing bacteria to exist. Removing or disturbing this speeds up the process of erosion and the topsoil ends up in the Skykomish, or whereever.
If you feel you absolutely have to do it, use a handsaw and saw off the stump as close to flush with the ground as possible. If you have to use a chain saw, then it's too big and you should leave it as is and work around it with creative pad placement and spotting as others have stated above.