First: can it be done positively?
Before talking about cups or jaws, another question belongs at the start: does the part have a rim, a hole, a contour you can reach under? Positive locking holds without force, does not fail on pressure loss and is independent of whether the surface is oily, dusty or damp. Where it is possible it is the safe and usually the cheaper route – and it is regularly overlooked because cups and jaws are the more obvious images.