Recommendations for handheld documentary/social/street/photojournalism? + OM-D E-M5 or GH3

It depends totally on which video camera you're talking about.  If it's a RED Scarlet or Canon C300, then yes, you'll likely get better video quality than a GH3.  If you are talking about a camcorder like a Canon VIXIA M41 or even Canon G10, the GH3 will be significantly better, as will the GH2, hacked or unhacked.  The superb resolution, high bitrates, and shallow DOF because of the large sensor, and 24p are going to give GH3 videos a much more cinematic look.

Beautiful test video of a GH3

https://vimeo.com/51928527

That's why almost no professionals doing video stock or indie films are using small sensor video cameras anymore.  The compact camcorder is strictly a vacation or birthday party camera these days. Small sensor professional video cameras like the Canon XA10 or Panasonic AG40 are still used for ENG or documentary/news videographers, but they are quickly being replaced by DSLRs like the 5D3 and large sensor pro video cameras like the FS100, C300 or Panasonic AF100.

As far as Tedolf's question, if you are going to be doing mainly stills, perhaps the EM-5 might make sense.  If you are going to shoot a lot of video, or want to get into video production, the GH3 is the obvious choice (it looks to be an awesome camera).

Best to all, Markus