GH3 sensor quality

How does the GH3 sensor compare to the OMD with regards to:

• Shadow noise at low-ish ISOs?
• High ISO noise?
• Dynamic range (highlights)?

I was initially turned off by the size of the GH3, and had decided to get an OMD. But if the GH3 provides better overall IQ, then that may be the way to go for me.

FWIW, I only shoot raw and I sometimes do quite a bit of post processing to my images with regards to contrast adjustments (shadow boosting, highlight recovery, etc).

Been searching around and couldn't find a definitive answer to my questions, aside from speculation that the GH3 and OMD share the same Sony-made sensor.