These guys primarily focus [heh, heh] on still photography, but here's their video review of the Panasonic GH4. Others may find it interesting - particularly the comparisons with Canon & the Moire discussion.
you can flatten the crap out of the GH4. I doubt if it is technically proper S-Log, or whatever it is called, but it has some built in LUT style settings where you can lift or lower blacks or highlights with a 0 to 5 curve, together,, seperately, and save as presets. I have not tested enough to see how clean this ends up on the 8 bit recordings, and realistically, one has to balance flat contrasting with what you are left with in 8 bit and make sure you are not hurting the end result by flattening too much.
But, yes, you can flatten the GH4. Hopefully, the color tone on those canon C series is not so red/orange like their DSLR, but so far, GH4 isn't suffering from that. The color just looks SO RIGHT most of the time coming out of it.