Sony a7 vs gh4

the A7 doesn't have the same XAVCS codec that the A7S has so video is undoubtably stronger on the GH4 in 1080p with both 100mbps and 200mbps options (100 is better IMO for most scenarios)

They are both great cameras. One thing to consider is what lenses you own. You're going to be dealing with the 2x crop factor coming from full frame to micro four thirds.

Both of these cameras will produce great images. The a7 will preform better in low light, it will have better dynamic range, and better depth of field. GH4 does internal 4k and UHD, it should also beat the a7 in terms of detail. GH4 battery life seems to be a bit better, and for photo GH4 wins in burst mode. GH4 will record 4:2:2 10-bit to an external recorder. The a7 will spit out a 4:2:2 file externally, but can't confirm what the color bit depth is, I'm assuming its only 8bit but it can possibly be 10bit. Internally the a7 only will give you 24mbps at 24p and 28mbps at 60p. The GH4 internal recorder will give you 4K at 100Mbps in IPB compression and Full HD at a max of 200Mbps. HD can also be toned down to 100Mbps IPB or 50Mbps IPB.

Hope this helps!