IMO, the Blackmagic will be a superior aerial camera in terms of image, larger sensor, editing friendly codec, and most importantly, the global shutter. Of course, I haven't seen or tried the GH4 yet, but to get the same quality files out of it, you will need the expansion module, bringing the weight and price past the BM. In the "real world" it's probably not always necessary to have the higher quality files, but sometimes it's those specs that matter.
But then there's the 60p of the GH4 which some people require.
The battery situation of the Blackmagic is terrible for aerials, because to work for a whole day you need to power it from the gimbal battery, and then the internal is really just dead weight.
I think to a potential client the blackmagic seems like the more professional camera to use. There's still a stigma attached to the smaller DSLR's.