D800 - buy 16-35mm f/4 or 17-35mm f/2.8

I'm replacing my D7000 with a D800. As a result, I have to replace my 10-24 Nikon DX lens. I'd like to use ND filters so I'm not really looking at the 14-24mm, which can't take on a screw-on filter. I'm deciding between the 16-35mm f/4 and the 17-35mm f/2.8. I split nearly 50/50 of my shooting between landscape work (usually on a tripod) and sports photography (triathlons, swimming, running events). So, I'd like a sharp lens that is also fast.

Here are my thoughts on each lens. Any help?

16-35mm f/4 - VR is nice when I hand-hold shots; distortion is awful at 16mm; slower lens than the 17-35mm f/2.8

17-35mm f/2.8 - no VR; faster lens than 16-35mm; limited distortion

Thanks!
-Dan