This is a contentious title. I'm not sure whether to post it here or in the Sony Forum (or, indeed, in both).
I usually don't posts comparison threads - but this is a burning question to me. There are, of course, lots of other issues (ergonomics, ISO, fun-ness, weather-sealing etc. etc.).
dPreview have very neatly dealt with the ISO question you can check it out here
Weathersealing is obvious (OMD is, Nikon Isn't)
Ergonomics is really a matter of taste.
Reslolution is a point at which the NEX should be a clear winner. I just wanted to get a handle on how much better it was.
So - let's make it a little fun (although you'll only need to think for two ticks to see which is which).
I'm presenting three pairs of shots - screenshots from the Lightroom XY bit. The first shot is the whole image (I've topped and bottomed the OMD images to 3x2 to make you think a little harder) - with a 100% crop underneath.
All were shot at base ISO, f4.
the Sony were shot with the Sony 50 f1.8, the OMD with the Zuiko 45 f1.8. The hedge shots were handheld, the bike shots on a tripod. One of the bike shots was taken at the same distance (which gives roughly the same magnification at 100%) the other (of the whole bike) the tripod was moved to get the whole bike in to the frame lengthways.
I'm not really sure what to say . . . . . . so I won't say anything!