Especially when you include price constraints, it's a hugely complicated question, and you don't give us much of the information needed to address large parts of it.
There's even
more differences in personal style in video than in still work, I think, and what the cameras are good for varies a lot. There's also often more question of fitting in with the rest of the team, because video is much more often a collaborative effort than a standalone one.
Now that Panasonic has started doing things with IBIS some of the decisions might get easier...depending on what you're doing. I find I work a
lot with handheld video, even using rather long lenses, and IBIS is part of what makes that possible. But if you work more with traditional camera supports, IBIS is almost irrelevant.
Similarly, if you want to produce one-shot YouTube specials, you need
very different sound support in the camera than if you're intending to compete with Hollywood dramatic productions (where the sound is all recorded separately, and often created after the video is shot).
4k is the hot thing, and utterly vital if you're aiming for the big screen. But unless you're most of the way there already, you won't
get to the big screen on your next project, or the one after that (and if you are already most of the way there--you don't need my advice, and probably not the advice of most of the rest of the posters here either) . 4k can be useful for productions released at HD, too--often as a substitute for better technique (when you reduce the resolution you can make lots of flaws go away, and you can use the extra space to fine-tune framing and do more with stabilization in post). So mostly it's
not the cost-effective way to produce HD product.
Also the data storage needs of 4k are pretty terrifying.
While I'm all over the credits
here, director of photography (and operator of one of the cameras; we had 6 running during the live concert) are the ones relevant to this. The release is on DVD, BluRay, and direct download, and we have sold
far more of the DVD resolution versions. It was shot at 1080, and edited at that level, but on say a 46" 1080 TV the DVD version looks surprisingly close to the actual 1080P version (DVD supports a maximum of 720x480 pixels).
I shot my part of this with an Olympus OM-D EM-5 (not the newer mark II), using lenses from 14mm to at least 200mm, nearly all handheld. There were drawbacks to working with that camera (but it was what I had that did video). The drawbacks weren't mostly serious for the particular use I was making (roving photographer at a live concert shoot), but would have been in other scenarios (needing longer run-times, say, or more adjustment of exposure or focus within a shot). The results looked mostly better than video shot with a dedicated Panasonic HD camcorder or with Panasonic Micro Four Thirds GH2 or GH3 bodies at the same event. But pretty much nobody, including me, would have given the EM-5 the nod as the obvious choice of camera for that particular situation.
So, the basic advice if you're getting started: get something decent that's part of a viable eco-system so far as you can tell for your interests (Micro Four Thirds for video: seems possible to me),
don't break the bank, remember that this first investment is just getting your toes wet -- and go out there and shoot and do things with the results, and the
next time you're choosing, you'll know a lot more about what you do and don't like
and why, and can make a better-informed choice. (If you already have extensive video background, my apologies! I don't read the initial question as telling me that, so I didn't know.)
Here in the UK the GH5 body comes in at £1690 , the G80/5 comes in a just £580 just over one third the price of the GH5
