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

Everyone agrees that the Nikon D4 is ideal for holding doors open whereas an old CD-format camera is best for throwing like a frisbee. For affordability you cannot do better than a 2006 Kodak Easyshare.  Maybe specify your needs, Louis?

I will go out on a limb and suggest that the GH3 has better video features and a more useful control layout (e.g., bracketing) whereas the OM-D has an IBIS advantage.  The sensors are both quite excellent and seem to satisfy pixel peepers.  Panasonic now has a wireless flash protocol, negating a pretty major negative as far as I am concerned, so it really is down to IBIS-and-size versus video-and-control-layout, plus other things that are minor for me (but maybe not for other people!).