empedocles

XT4 and XT3 are the same IQ wise. 

Having owned both the S1 and XT3, I can say the S1 dynamic range is better, better in high ISO's. The image is more natural than the XT3, less sharpening and less noise reduction going on.

I like the Fuji color presets a lot. If you are shooting in LOG you kind of lose that edge, as the color on Fuji log isn't particularly easy to work with. Eterna is really nice though. Fujis HD 120fps is better than Panasonics. 

 

Full frame, more dynamic range, better low light, better built, better ergos, IBIS for both stills and video, plus with the latest firmware, more capable as a ‘cinema’ camera if you wish to rig it up and record externally.
In regard to the latter, I don’t, so it doesn’t make any difference to me.
Fuji wins for me on; size (but needs at least an aftermarket bracket grip which cost peanuts and in fact I have 2 to give away for the cost of postage EU) and SOOC colour science if you do not shoot log.
A better comparison is the XT4 as that has IBIS.
S1 vs XT4? I would choose XT4.
S5 vs XT4? S5 for me.
The ‘issue’ that some struggle with is the lenses...
Fuji make many, but none really float my boat. If I had to pick one, I’d go 16-55mm f2.8 ‘one and done’ giving a full-frame equivalent range of 24-83mm.
Panasonic get criticized for a lack of full-frame lenses and that most are too big and heavy and to an extent this is true...but smaller primes have begun to appear and all the Sigmas and Leica’s (budget busters for most) etc.
I’m happy with the pairing of Sigma’s 28-70mm f2.8 which is shorter in reach than Fuji’s equivalent but the Panasonic’s can all do APSC crop mode turning the 28-70 into a 28-105mm.
To conclude, the package of S5 + Sigma 28-70mm is no bigger, actually lighter and more capable than the pairing of the Fuji XT4 + 16-55mm. Just...
Couldn’t go wrong with either!
I do prefer primes but that for me means more bodies as I need multiple focal lengths at the same time so use 2 bodies (need a third) and 5 lenses.

The Panny S1 is ‘probably’ the best value bit of kit available right now, just pipping the Fuji XT3, but unless size & weight is more important, S1 for the win.
However, if size & weight is a factor, Pannyboy S5 over the XT3.
That’s where my money would be going, Panasonic or Fuji.

A used Panasonic s1 is like $1500. Great camera with vlog. 
Internal 6k open gate full frame 10bit, 4k 60 10bit, Prores Raw over hdmi. Anamorphic modes, amazing IBIS, great internal battery life (3 hours per battery) Full Varicam V-Log and Cine Color science. 
For what it goes for on the used market its probably the best bang for buck camera you can get currently. 

If you want to stick with Panasonic MFT (like your G6), and you don't care about the IBIS in the GH5/G9, then yes the Panasonic GH5S would be your "best" choice. (for maximum bang for buck though, consider also the Panasonic G85)

But if you're to consider other Panasonic choices then consider: Panasonic S5 or S1 (or even S1H, if you have the cash). 

But if you're to consider other MFT choices then consider: Z Cam E2-M4 or BMD Pocket 4K. 

I could be wrong but I think the K is for the package that comes with the kit lens while the other one is body only. No difference between the cameras themselves.