I am generally happy with the image quality of the E-M5, but make no mistake about it, you can not bend the rules of physics. The larger sensor in the same sensor generation will always have an advantage over the smaller sensor, and there is no question the NEX-6 has cleaner images, especially in low ISO. This is not to say the image quality of the E-M5 is bad; it's just not as good as the NEX-6. Not something I concern myself with.
I actually prefer the handling of the NEX-6. It has a larger hand grip, and the controls are easier to access. I am so used to be able to hold the camera in hand, and turn the camera on or off with my index finger. There has been a few occasions where I missed shots because I was fumbling with the power switch on the E-M5. This camera requires two hands to turn it on or off. I know I can leave the camera on and let it sleep, but this uses more power and I only have one battery at the moment. Also, if it powers off automatically (at the set time, say 30 minutes), you will have to physically turn the camera off, and then on again to turn it back on.
My other beef with the handling is the small buttons. Even without gloves, I find it hard to use the 4-way switch at the back. My thumb keeps hitting other buttons. Understandably, this is a small camera so there isn't much can be done. I find the implementation is better done on the NEX-6.
Other things I like better on the E-M5 is the dual wheels on top of the camera, to control the aperture/shutter speed, among other functions. The placement of the Fn2 is excellent when it's assigned to magnify view. The memory card has its own door, whereas the NEX-6 has the card slot inside the battery door, and I cursed the #$%$# thing whenever I try to take out the memory card, because the card is not easy to grip and remove.
Being as good as the EVF in the NEX-6 is, it's not without shortcomings. For one thing, in high contrast scenes, the shadows tend to block up and becomes hard to focus. With the E-M5, the contrast in the EVF is dialed way down, to a point that if you are trying to focus on something with low contrast, it's very hard to do. The good thing is opens up the shadows and you can see a lot of details in the EVF. I do prefer the E-M5's implementation.
Even though the NEX-6 has a higher resolution EVF, honestly, I didn't notice much difference between them. The E-M5 seems to have a faster refresh rate and thus better and easier to see at low light.
I have only one auto focus lens for M4/3. It's the excellent Panasonic 14-45 kit lens that came with my Panasonic G1 and I only shot a few test pictures with it when I bought the camera. For sure, the E-M5 beats the NEX-6 in quick focus and low light performance. Even in moderately good light, the NEX-6 has trouble locking focus. I see that the A-6000 has a much improved AF system, but frankly, AF is just not that important to me, at least at the moment.
This is the area where the E-M5 shines. Its In-Body stabilization system is fantastic and is as good as lens based systems, except, perhaps with very long lenses. I am completely blown away by its effectiveness. Best of all, it works with ALL lenses mounted on it. The E-M5 wins hands down.
The NEX menu system is chaotic. It seemingly has no organization and finding anything in the menu is a challenge. The E-M5 is much better, but due to its endless configuration possibilities, it's not the easiest to understand. The good news is that once configured, there is little need to go in the menu again.
Obviously, it's much easier to find manual focus wide angle lenses for the NEX-6 than the E-M5, due to the larger sensor. But on the telephoto end, the E-M5 wins. So depending on what your needs are, this could dictate your decision. To me, owning both is the best. NEX-6 for wide angles, and E-M5 for long lenses.
Both are great and capable cameras with its own strengths and weaknesses. For taking pictures with manual focus lenses, I prefer using the E-M5, simply because the In-Body stabilization is so amazing, you can you use the majority of c-mount lenses without severe vignetting. On the other hand, the NEX-6 gives you wider angles on the same lens, and has better image quality. You can't go wrong with either camera; it all depends on what is more important to you. Ideally, keep both on hand, and use whichever you want :)
Lamp Post - Olympus E-M5 & Jupiter-3 5cm f1.5