I have no direct experience of those lenses, but I feel qualified to give some advice. If you've got to do lots of walking around, carrying kit, then go for the lighter lens, which I am sure will be the f4. I've shot a Nikon 70-200 in various guises over the years, but when I broke the last one (they get a LOT of abuse) I went for the 70-200 f4 for the weight reason (also half the price). No regrets at all. One stop less of light capturing shouldn't be an issue, and the loss of some bokeh is more than made up for by not being knackered.
Regarding golf though, do you reckon 200mm is enough or do you have something longer as well? When I've shot golf I've placed myself at positions where I can cover a couple of greens and a couple of tees at the same time, but with a 200-500mm lens on a crop sensor body. Sit down, monopod, watch the players go by.