Do you use an add-on grip with your D850? If so, the size of the Z9 may not feel that big. If not, you will find that the Z8 feels a lot like a D850 in size and the Z9 feels a fair amount bigger. (I shot the D850 and D500 before going to mirrorless.)
I have both a Z9 and a Z8. I like them both. IQ, AF performance, and FPS are pretty much the same. Firmware updates are not synched between the two cameras and there can be differences from time to time (and some differences are related to physical differences between the two bodies.) It's quite possible that I would have bought two Z8s rather than a Z9 and a Z8 had the Z8 come out at the same time as the Z9.
I do not find the battery life is an issue with the Z8. I always carried an extra battery or two with the D850 and D500. Now I usually carry two extras, if going out for a day.
A couple of other differences beyond battery size/life and body size/weight. The Z9 has a built-in GPS, which I like at times. I like that the Z9 has more customizable buttons, especially that it has a third button on the front of the camera. I also like that the Z9 has two CFe card slots, whereas the Z8 has a CFe slot and an SD slot. Of course, on the latter point, if you want to use SD cards, then you might prefer the Z8 configuration.
Being larger, the Z9 may balance better with bigger lenses. However, I've had no issues using the Z8 with the Z 400 mm TC lens and the Z 800 mm PF, my two largest lenses.
Being larger, the Z9 has better heat dissipation. This probably matters more for longer video recording at higher resolutions than for stills.
Both will work well with your F mount lenses using an FTZ or FTZII (FTZII works better ergonomically with the Z9 than the FTZ). Both bodies will require a good fast CFe card to get the highest performance offered by them for FPS and high resolution video.
Both cameras are great. So hard to see a wrong choice.