The G7 is very nice in your hands. It is like a little baby DSLR. The GX80 is newer so probably better video, but it costs more and doesn't feel nice to hold for me.
Either are very compact especially if you use Panny or Oly lenses. If you really do want a 3.5-5.6 12mm-24mm lens you should be able to get the good Panny 12-32mm pancake lens in a kit with the G7 or GX80.
But most people would recommend getting body only with the Panny 12-35mm constant 2.8, or the Sigma with Speed booster option (both much more expensive).
If you dont need a fast lens much the 12-32 with the 35-100mm 4-5.6 (might be able to get both of these lenses in a kit) and the Olympus 45mm 1.8 is a good kit imo (will probably get a fast prime between 17-25mm too). Total cost approx. £640 all new except the Panny lens which was bought used but as good as new.
It seems that GX80 is more for people who need stabalisation. And the G7 is better ergonomically (fully articulating screen, nice dials etc...). You may miss Canon colours but at least you will have 4K video. Keep an eye out for Panasonic cashback offers (they currently have a £100 one).
I used to love the colours and general image from my 600d (t3i?) with or without Technicolor Cinestyle. If you dont need 4k maybe just upgrade to a newer Canon or look at the Canon XC10. If it was me I would go for a Panny to be future proof in terms of resolution and you can use nearly all lenses. The colour is still decent enough. The strange bright green and red on GH4 seems to of improved.
