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[Yep, from the investigating I've done the sensors in the GH2, GH3, and OM-D are all created more-or-less equal in terms of Rez, DR, and Noise handling
The GH3 and OM-D are more or less equal in terms of resolution, DR and Noise. The GH2 is close, but not quite at that level in the noise department (similar up to around ISO 1600, then the newer cams take a noticeable lead, especially in color accuracy at high ISOs). The GH3 and OM-D are also noticeably better in the DR department over the GH2. DxO measures it to be about a stop, but in practical use, it feels closer to two stops in my experience.
That said, for most shooting, you'd be hard pressed to tell a difference between all three...it's only at the extremes of their abilities that the differences become apparent. While I love my OM-D (and I'm finding it very hard to use my GX1 now since I'm so used to the OM-D's awesome IBIS), I do have to say that Panasonic is still by far the best when it comes to autofocus...it's both faster and more precise than the OM-Ds, though the OM-D's is still quite good.