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The OM-D does show a lot more noise in your example. However its a fairly massive crop - maybe 4 to 1?
There is more noise, but I think you would need a fairly large print to see it. Still, I definitely find the 6D better at high ISO than the OMD. The IBIS and fast lenses for the OMD make up for much of this deficit. However, when shooting indoors or flash I still prefer the FF output of the 6D.