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I own the EM5 and the Nex5n (which I choose after a shootout with the 7) and if the EM5 could do 60p in video mode, I would not own a Nex camera. Both are great and have individual strengths. IQ is pretty much indistinguishable between the two, the EM5 sensor is amazing. Lens selection is a big advantage with M43 as Nex lacks fast zooms and the prime lineup has holes.
Some EM5 pros/cons: 5-axis means all lenses are stabilized in photo and video mode, and its superior to Sony's OSS IMHO. With the grip you have options for extra controls and two batteries, the OLED screen is bigger/better than Nex, EM5 shutter is much quieter, live bulb takes the guesswork out of long exposures, touch focus/shutter makes it easy to shoot candids without looking like you're shooting and the video quality is surprisingly good though limited to 30p - its actually better than the A99 that's I'm currently testing - see below. It has fantastic weather sealing as well, get a sealed lens and you've got a great worry free kit. It's not all rainbows and puppy dogs though - the EM5 is a bit of a pain to get setup as you can customize everything, some features are buried in menus and there's no built in flash.
Some Nex pros/cons: more video framerates though not any better IQ wise, sweep panorama makes great pano's a snap, it has a few tricks to take great lowlight/HDR shots (jpeg's), body is a bit smaller but lenses are all pretty big, focus peaking is unbeatable for manual focus, with a Metabones adapter you have full control of Canon lenses, touch focus shutter great on the 5n as well - though I don't know if the 6 has it. Nex cameras are saddled with Sony's goofy consumer icon menus which are a bit of a pain and I find Nex controls to be inferior to the EM5's
Here's a short test video I did with the A99 and the EM5, full screen at 1080p you can really see the difference.
Here's a series of comparison images and a lot of Dpreview troll BS.
I keep the 5n because its a cheap/small backup that I can use with any lens via adapters and it shoots 60p. Since getting the EM5, I don't shoot stills with the 5n anymore. I kept it to be a companion to the A99, but its video is so dreadful I may be returning it and heading back to Canon - if I do I'll get a Metabones to get 60p on Canon lenses with the 5n.