I've shot both. I own the 500 + 1.4x TCIII and think it is an amazing combo. I have the 800 f6.3 POF on order.
A good friend lent me his 800 f6.3 PF for over a week and it is an amzing lens also. However, it is only 1/3rd of a stop faster than the 500 + 1.4x TCIII.
I then also wonder why I really need the 800 when I can get results like this from the 500 + 1.4x TCIII.
Best to click on the images to see them at full size.
Z9 + 500 pf + 1.4x TCIII, 1/400s f/8.0 at 700.0mm iso125
Z9 + 500 pf + 1.4x TCIII, 1/500s f/8.0 at 700.0mm iso1000
Z9 + 500 pf + 1.4x TCIII, 1/320s f/8.0 at 700.0mm iso900
Z9 + 500 pf + 1.4x TCIII, 1/640s f/10.0 at 700.0mm iso250
Z9 + 500 pf + 1.4x TCIII, 1/320s f/8.0 at 700.0mm iso220
Z9 + 500 pf + 1.4x TCIII, 1/640s f/8.0 at 700.0mm iso1250
Z9 + 500 pf + 1.4x TCIII, 1/400s f/8.0 at 700.0mm iso3200
Z9 + 500 pf + 1.4x TCIII, 1/400s f/8.0 at 700.0mm iso6400
Z9 + 500 pf + 1.4x TCIII, 1/500s f/8.0 at 700.0mm iso160
There is no doubt that a dedicated lens is better and one without the need of a TC, but I am astounded how good this combo is and the AF works brilliantly.