Why don't you buy both used, see which one you like better and then sell the lens you don't prefer. I have a 70-200mm f/2.8L IS mkii and I'm quite fond of it.
Why don't you check lightroom to see which aperture you shoot at when you take the 70-200mm f/4L out on the town. If it is 200mm 90% of the time... save the cash and buy the prime. If you are constantly adjusting the focal length... then you have your answer.