Hi Morgan,
I would choose canon for video / filming. Out of the box I would say both the canon and Nikon are fairly similar, however canon has Magic lantern, which can be used on the 5DMK3 and it works very well. Recently a new raw video feature was released allowing it to shoot 14bit raw video at full HD at 24p. wow, It really shows how much these companies hold back on the firmware of these cameras. ML enables all the features of this camera that SHOULD already be there (they were also able to enable this raw video feature on the 50D which doesn't even have any video features). ML also includes a ton of other features for normal still photography. Nikon or any other brand has nothing to this for a full frame.
just google 5D mk 3 raw video or read this:
http://www.canonrumors.com/2013/05/5d-mark-iii-raw-video-a-case-study/
