That's why I kept them both
. My first 500 was the f4G and I got the 500PF just for one reason: Being more agile and mobile.
Going for a hike with a 500mm f4 is - or at least becomes - pain if you are not built like a tank yourself. Doing it with the 500PF hanging off a strap or being hooked in a waist belt is just great. I have even used them both side by side occasionally. Just recently I had the D4S with the 500f4 set up on the big tripod for the primary target that was expected to appear in a dark corner at the border of the forest. The D7200 with 500PF (giving you 750mmm f5.6 equivalent) was laying beside me and the small tripod was prepared for it in case I spot something through one of the other tent windows that I couldn't reach easily with the big gun while waiting for the star to show up
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Yes, with the 500PF you loose a stop of light, it will make the noise level raise in dimmer conditions and make your backgound a bit less smooth - especially if using a DX body.
But as always the question is what you do and how you are doing it. It all comes down to whether you nail the shot because you are quick enough or you could have got it if ...
I use the 500f4 with or without TC primarily on tripod or monopod, when working more stationary and go for dedicated targets and use dedicated locations, especially if I know light will be an issue. This doesn't mean that the 500 f4 is not walkable though, especially if the lighter and less front-heavy E version (I have "only" the G) is used.
When I am hiking (e.g. "beach combing" or on a mountain trail) I prefer the 500PF because it is a breeze to handle, no matter whether you shoot it handheld or using as a support whatever you find around you. I even managed to combine the 500PF combo with one of the big GorilllaPods to let it hang off a branch or clamp it to a rock. No way doing things like this with the 500 f4 ...