Why is the EM5 so much more popular than the GH3?

That is an answer, and this is an awesome. I like to have a camera with real grip and large battery inside, with well laid off controls, and well balanced. And, because you've mentioned weight, check it out. I agree to have all mentioned goodies for a few extra ounces.

And believe me I'm not the only one...

If you're for smaller size and weight, there are smaller and lighter cameras than E-M5 out there, even between M43 cousins.

OMG, I forgot to mention remote control capabilities using cellphone. Just this single feature make a huge difference.

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Looking for equilibrium...