I have very, very little experience with underwater video, but from that experience and from what I have read, it is very difficult to do a good job "mixing" video and stills. They require a different mindset, different subjects, different lighting issues and so on. So, I have never worried much about video on my stills camera. I have a gopro and have played with that a bit and on occasion will take that on a dive instead of a stills camera. If video was more important to me and especially if I felt I needed high quality video and photo in one camera I would get the GH4. But for now I will, from time to time, take a short video with my stills camera on a dive, but it is just a minor thing.
I am sure there are those who can readily switch from taking nice stills to taking nice video and back again, and I am sure there are even more who would insist they can do that, but for me that just isn't what I am looking for.
FWIW, although I cannot judge this for myself, I think the video ability of the E-M1 is not so bad:
http://www.eoshd.com/content/11895/first-look-olympus-om-d-e-m1-vs-panasonic-gh3
It wasn't long ago folks were raving about the video from the GH3. I suspect the E-M1 is capable of producing can take much better video than I can shoot.
I think if I wanted a camera to "take along" on dives rather than really having a goal of doing dive photography, I think I would get a Canon S120 or Sony RX100 and Nauticam or Recsea housing. I'd use a ULCS tray and single handle with an Inon S2000 strobe and then either have a red filter I could attach for video or maybe use dual handles and put the strobe on one and a video light on the other. That choice might change with a bunch of new camera models coming out between now and Photokina in September.
Something like this could be really interesting as a "take-along": http://camyx.com/rumors/2014/07/new-panasonic-lumix-lx8-specs-leaked/