My 200-400 was consistently better on my Z cameras than on my DSLR cameras. On DSLR cameras it was good, but not quite sharp at the long end, with distant subjects, or with teleconverters. With the Z cameras it was great at the long end and with teleconverters as good as the base lens. As a result, I'm not in any hurry to sell the lens even though I have the Z 400mm f/4.5. The Z 400mm is better, but the 200-400 is very flexible and a good option with the TC covering a lot of situations.
I'd describe the AF on the Z cameras as significantly more accurate - not that any of these lenses were bad on a DSLR. But the consistency of accurate AF combined with the minimal need for AF Fine Tuning is a big plus.
The other aspect of this is AF Fine Tuning. While not mandatory, AF Fine Tuning was relevant to DSLR cameras. Fine Tuning is always done with the center sensor, even though outer AF sensors might be slightly different. There were also issues with different fine tuning results at different focal lengths. That's all largely gone with the Z cameras. You can use any AF point in the frame and get consistent results with accurate AF. You can use any focal length and focus is accurate. And you have the benefits of the EVF - focus peaking, magnification, and WYSIWYG viewfinder. I find manual focus is easier with the Z bodies than it ever was with F-mount bodies.
One final issue is with the age of the lens and teleconverter. The most recent F-mount lenses are similar in sharpness and performance to Z-mount lenses, but the Z lenses tend to be better in the outer areas of the frame. You also get better TC performance when pairing a lens and TC from the same time period. But in general, older F-mount lenses are more likely to need AF Fine Tuning on Z cameras - albeit at lower values than on DSLR cameras.