Back when I experimented with push/pull and stop as weapon effects, I found that when an object wasn't using thrusters (eg. inert) only push or pull would affect the object. Stop didn't actually stop the target object. From this I have assumed that stop cancels thrust effects but doesn't change the movement of something from momentum. But push/pull affects the momentum of the target hit. So for a tug push and pull weapons are useful and stop a waste of time.
However this was a while back and it might have changed since then.