Mike
That is an interesting question.
When I think about it, I think about some of the major championships that I have played in because that is where I am really trying to score my ball and the greens are the firmest and fastest.
The one course that comes to mind the most is Seminole during the Coleman Invitational each year. The members take great pride in having the greens EXTREMELY firm and fast. They like to sit on the hillsides and watch approaching shots to the greens and when you approach your putt, you can hear them laughing about the impossibility of getting your putt to stop by the hole. So, at least during that event, I think the green firmness and speed TOTALLY dictates the strategy of how you play some holes....which would be different if the conditions were less demanding. Seminole is not a difficult course unless the wind is howling and the greens are not treacherous unless the wind is howling and they are stimping around 14-15, like they are during the Coleman.
One example of this would be the 14th hole. It is a shortish Par 5 with a raised green surrounded by bunkers, with a big deep bunker fronting the green. While most of the field can reach the green in two shot because it generally plays downwind, most of the field will lay up to 8-100 yds short when the pin is located in the front third of the green. The reason why, is because downwind it is impossible to stop a long or mid iron below the hole and from above the hole, even a 20 footer is quite likely to be putt off the green down into that fronting bunker. So players learn that they have to be below the hole to even think about a birdie and if not, they are just hoping to make par. Seminole has other examples like the 3rd hole, another Par 5 where even a short chip shot may not stay on the green even if you a chipping up hill if you catch the wrong contour trying to get the ball too close.
What I am trying to say is that yes, the firmness and speed of the green surfaces can very much dictate the strategy of how one plays certain course. Without that at the Coleman, the course would yield very low scores by many players. As it is, there is only an occasional great score shot, usually on one of the tournament days when everything just went right and the safe strategy worked to perfection.