I've had both GX and GH bodies -- I wish they'd named them just A, B and C to make it easier to keep them straight -- but I think the G series is basically a simpler subset of the offerings in the GH and GX bodies. I suppose you could think of it as the Nikon 600 as opposed to the 810. The GH and GX series are more enthusiast-oriented bodies, with GH optimized for video and sound, and the GX for stills. BUT: some people like the GH for stills because they like the form factor better. It's still pretty compact compared to typical DSLRs, but it's quite a bit bigger than the GX. The new GX will be larger than the current GX7, but not a lot; it will have a 20mp+ sensor as opposed to 16; it will have better image stabilization for some m4/3 lenses; and, importantly I think in an enthusiast camera, it will be weather sealed.
Basically, I think the GH and GX lines may continue to diverge, with the GH getting more and more emphasis on video, while the GX continues as primarily a still camera. Some of the Panasonic lenses are already optimized for video, and while they're completely usable on the GX or G series, I think you'd be paying for qualities you don't necessarily need for stills.
I gave my GH bodies to my son, because he does both video and stills. I kept the GXs. I prefer to have my bodies in the same style (I have one silver, one black, and tend to put longer lenses on the black) so that I don't fumble them. You might decide to stay in the same body style for the same reason, or you might prefer to have two different styles, one for ordinary shooting, and then the GX for when you want to be more discreet. (The GXs can very discreet, when using, say, a short black zoom on the black camera.)