I think the shape of the basic frame is moot so long as the angles (motors from the FCB) are the same.
Flight characteristics are dependent upon how far apart the motors are (further is more stable, closer is quicker) and the motors/electronics you use versus the weight of the copter.
The BatBone can come in a kit or you can get/build your own mounts, struts, booms and rear motor pivot. The original body, has no kit option. You can buy the mounts etc piecemeal from FT or you can put together your own but there is no kit with all the parts.
The BatBone most likely weighs more but the weight difference should be very minimally impacting if you are building a beefy enough copter for video.
As Loc8tor stated, both will use the camera vibration mitigation mount (awesome piece of hardware, no jello in your video at all).
The BatBone costs more.