I'm fairly certain a fight between Diavolo and Jotaro or Dio would depend on who triggers their ability first. Because, the way I see it from what we know about King Crimson, it erases time, but that only applies to time that occurs after it is activated. If Jotaro or Dio were to trigger a time stop before Diavolo can activate King Crimson's ability, he can't trigger it in stopped time (because as far as we know, he can't perceive stopped time, unlike Jotaro or Dio, who have it as a necessary secondary ability in order to even use The World in the first place), therefore he is completely vulnerable. Jotaro would just break his limbs and retreat out of King Crimson's melee range, whereas Dio could either knife him to death outside of King Crimson's range or donut Diavolo outright.
Also, extra wrinkle in this discussion - consider the potential scenario where Dio wins in Part 3. His ability to stop time would've extended beyond ten seconds, possibly to the point where he can stop time indefinitely, as he himself speculated, meaning he could out-time Diavolo if a fight between them ever occurred by triggering The World at a point where he knows King Crimson's ability isn't active. That, and vampire powers make it so he can regenerate his wounds, meaning if Diavolo doesn't kill him right off the bat, he is screwed, because Dio will be like "oh, this guy can do some weird shit with time too, I better put a stop to that."
Of course, I should note that we don't know if the time elapsed during time stop is counted as part of the time skip. Assuming it does, that still means Jotaro/Dio can essentially nullify a good chunk of the time skip at least and make it significantly less effective, allowing them to more easily overwhelm Diavolo with their stands, which are basically the strongest known stands in terms of overwhelming close-quarters capability.