I'd take the Z 24-70 f/4 over any F-mount version in terms of image quality - especially midframe to corners. Center sharpness is not an issue with F-mount but the corners have some drop in sharpness. I also have the Z 24-70 f/2.8 and it's in a different league. It's excellent wide open, and midframe to corners make it the best of the bunch. The lens is truly outstanding with nice backgrounds. The f/2.8 is probably the best zoom lens Nikon has produced covering that range. Of course, the primes are at a different level, so if you want ultimate sharpness, it's not going to be a zoom. I use the f/4 version when weight is at a premium or landscapes/people are not my top priority. When I want ultimate quality, I use the f/2.8. On trips I'll often bring both lenses and choose which lens depending on plans for the day.
Among the 70-200 f/2.8 lenses, I have had the VR, VR II, and now the Z version. The Z version is clearly the best of the bunch - both in the center and midframe to corners. It's also best in difficult conditions such as backlit subjects. The F mount 70-200 FL is very similar optically, but for the other two versions (VR and VRII) it's a good move to trade up to the Z version when budget allows. The 70-200 is my favorite lens - I use it for landscapes, portraits, sports, events, and equestrian. It's less important for wildlife - mainly environmental images and large animals at close range.