How important is video? The two models you mentioned are the two best video focused SLR types (neither is an SLR). But they are very different cameras.
The gh5 is a high end, weather sealed (if you use weather sealed lenses) video focused camera with a smaller m4/3 sensor.,
The A7s II is a high end low light specialist camera with excellent video capabilities. It is low megapixel (only 12mp), it is not super fast (5fps), it is full-frame.
The gh5 will have a "deeper field of view" (Depth of Field or DOF). The smaller the sensor, the greater the DOF. This is proportional to the crop factor (relative size of the sensor). This is good or bad depending on your goals.
The a7s II will have a shallow DOF. Making for much greater subject isolation.
With some cameras you can have both. The very high megapixel full-frame cameras. For example the Nikon d850 (super expensive, wish I had one) has 46mp in full-frame. It supports a 46mp full-frame and a 20mp 1.5 crop mode. This crop-mode is the same image as if you manually cropped the image in photoshop. So you can also get a 15mp m4/3 image out of every d850 image.
How I shoot.
I value stills over video, but I also shoot a lot of video.
For still I use a Nikon d750 24mp full frame camera. My backup camera is a Nikon full frame d700 (12mp). Nikon and Canon have by far the best lens selections and I like a nice collection of lenses.
For event video, I tried a Panasonic gh4 and gh3, I kept the gh3 because I didn't need 4k video and the gh3 was 1/2 the price. I paired the GH3 with a couple of primes (lenses with no zoom). So depending on where I am placing the tripod relative to the event, I typically use a f/1.4 30mm or 45mm f/1.8. I can record the entire multi-hour event on a single take.
For sports video, I use a Sony RX10. It is weather sealed. It has a decent f/2.8 integrated lens which goes from reasonably wide (24mm equiv) to reasonably long (200mm equiv). Like every other thing which is not a GH series camera (or a cam-corder) it can only record 29.5 minutes every time I press the record button. So I have to press it 3-4 times for a football game, twice for a soccer game, and so on.
I was tempted to get a f/2.8 weather sealed lens for the GH instead, but the Panasonic 35-100 f/2.8 is the equivalent of a 70-200mm lens and there were times where I was set up closer to the action and didn't want to change lenses back and forth. Plus the 35-100 cost the same as the rx10 (1000 for each). So budget played a role as well.
If I had no budget (or damn near no budget) for video I would get the Sony a7s II and Sony FE 24-240mm f/3.5-6.3 OSS for general use and the 70-200 f/2.8 for when I could plan my location better or the weather was nasty. But only for locations where I could re-start the recording every 30 minutes or so.
For locations where I could not re-start my recordings, I would get a GH3 and pair it with a couple of f/2.8 zooms and a few primes for low light.
But if some one offered to trade me a a7s II or gh5 for my less expensive d750, I would keep the d750. But that is because I go on photo outtings many more times than I go on video ones.
Example of subject isolation:
I wanted to show just enough of the background to hint at where he was, but the viewers attention to remain on the boy not the landscape:
I wanted to show more of the background in this one:
A large sensor camera can achieve deeper DOF if you want it to. A small sensor camera can never match what can be done on the larger sensors.