Two interpretations: 1) the green alone makes the hole great; or 2) the hole is mediocre notwithstanding a great green.
The Old Course: 12
Sand Hills: 3
You will need to explain these choices Michael. I would count both of these holes as outstanding. 3 at Sand Hills is outstanding primarily because of the green and its surrounds but of course it is a par 3 so the green is the primary feature of the hole. 2 might fit the bill but I like 2 a lot. 12 at the Old Course is outstanding because of its fairway bunkers, memorability, strategic choices and its green.
I also disagree with your category 1. If a hole is great because of its green, it is a great hole.