I like to locate inferior quality bucks than get them running straight away from me at about 500yds--then I just shoot their nuts off so they can't breed--It's really all about deer management.

seriously though, standing is almost always better--I submit though if I am forced to shoot offhand I would 10 times rather the animal be moving--doesn't have to be flat out running--just some movement helps me personally become steadier.
hb