An excellent comparison of these two cameras. These are easily the two most significant large sensor cameras for videographers with a sub $2000 budget at this time. Sony virtually owns the space in the $2000 to $3000 range with the A7 series.
While I have only had my hands on the GH4 briefly, it felt good in the hand. I’d not want to shoot with anything smaller. Since the GH2, these cameras feel very well made, and ergonomics are quite good. Battery life is good, and lots of support in terms of accessories.
Two things about Sony. They have a great record for well crafted cameras. However, Sony has a long history of creating devices as small as they can possibly be produced. Even at the cost of ergonomics and functionality.
I’ve owned a number of Sony cameras over the years, and there are two other areas that make Sony stand out. They have long been leaders in autofocus, and low light performance. Flaws and all, these are two very compelling points.