So which is better? "GH3" or OM-D?

I've never used a GH3, so it's difficult to say.  I have an OMD EM-5, so I can only go on the obvious differences.

The biggest difference for me is just that: size.  My foray into micro 4/3 from not having owned a camera at all was governed by my preference for a camera small enough to fit into my (admittedly large) coat pocket while not sacrificing image quality.  My first micro 4/3 was an EP-2 for this very reason.

I got very used to manual control quickly with the EP-2, and though I have a long way to go in shot selection and in actually using that manual control to create nice cameras (I have a long way to go in creative direction as well), I've found that the manual control on the OMD EM-5 is quick and easy to reach and use.  The image quality vs. the EP-2 was shocking -- at not a big difference in size, the EM-5 is starkly better at taking good photos.  It's a tool that instantly made it easier to get the photos I wanted, especially indoors.

If I had any interest in video, I might look at the GH3.  But realistically I would probably go with the GH2, as I would be using it almost entirely for video and wouldn't be able to justify the cost of the GH3.  That's entirely down to personal preference based on how I use my camera, though.  For a lot of people on here, the GH3 will be an excellent choice.

For several months the EM-5 has been unopposed as the top performer in micro 4/3, but with the GH3 there is a legitimate choice for the micro 4/3 user that isn't based entirely in image quality or even general camera quality.  It'll take a while to get used to the change and there's probably going to be some fanboy vitriol for a while, but it can only be a good thing for the system to get the luxury of choice.