If it were me, I go with the new PF f/4 lens. Just the drastic decrease in weight from the f/2.8 version means I'd actually take it with me some place. Plus it's small size won't be as conspicuous in public.
I had the older 300 f/4 D lens back in the day and really enjoyed it, but it was heavy and I didn't quite know what I really wanted to shoot with it (apart from the Blue Angels that came into town each year).
Outdoors I don't think there's a reason to get the 2.8 unless you absolutely need that extra stop and/or you're shooting sports. At the focal length, there's going to be plenty of compression at f/4 so that shouldn't be an issue either. And as others said, on a modern camera, f/4 should be fine since you have more ISO flexibility; I shot a concert in a dark club and captured photos just fine using a 16-35 f/4 lens.