Upload & Sell: Off
I went through a similar decision last week. You can see the thread here:
If you read to the end you will see that I finally decided to get my partner the OM-D, and a nice set of lenses. At the same time I recommended that one of her friends get the NEX 6, however, and if I were buying for myself I probably would have gotten the X-e1. There are strengths to each system, and how you feel about the ergonomics should matter. For my partner, who has small hands and fingers, the small buttons on the OM-D were not a problem. For me, however, I find them so small compared to my big hands that I can hardly use them. Although, even for her, the ergonomics worked better with top part of the grip. The OM-D also worked for her, because she wants and values fast accurate autofocus, but doesn't use tracking (i.e. servo) autofocus. She also enjoys macro a lot and m4/3rds has some very good macros (I got her the Olympus 60 f/2.8). At the moment, NEX doesn't really have a macro lens that competes, although I am sure when the Zeiss 50 macro comes out next year it will be great, but no doubt a lot more money too. So for my partner given how and what she shoots the OM-D was the better choice. It probably is if you want to shoot predominantly AF lenses.
For her friend, however, I recommended the NEX6. Her friend wanted a camera for two primary purposes, travel and portraits. The NEX6 is noticeably smaller than the OM-D, and should be very good for travel. I don't know how good the kit zoom is, but it is also nice and small. She should also be able to build a great kit by adding the new 10-18 for wide angle, the Zeiss 24 f/1.8 and a nice portrait lens. I will try to talk her into getting a Rokkor 58 f/1.2 for portraits, which ought to be spectacular on the NEX6, but it seems that even the Sony 50 f/1.8 isn't too bad. For her friends given how and what she shoots, the smaller size, and larger sensor (with the opportunity for greater depth of field) of the NEX6 seemed the way to go.
For myself, both the OM-D and the NEX6 are too small to be comfortable in my large mitts. When handling the cameras I found the Fuji to be a lot more comfortable. I also like the line up of primes that Fuji has developed. I think I could be quite happy with the 14 f/2.8, the 23 f/1.4, the 35 f/1.4, and either my Rokkor 58 f/1.2 or the 56 f/1.4.