My response was like two pages long with no end in sight, but I remembered I have alot of work to do so I want to TL;DR my response and save the long one for another day.
Having owned an X-E1 and NEX3, 5, and 7 I would choose between the X-E1/2 or the NEX-7.
The X-E1 has wonderful menus and controls, but it is a VERY slow camera in more ways than one. It is slow to operate, and slow to respond. I absolutely hated that camera and the really bad EVF until I checked my lightroom statistics at the end of the year and found that all my best images by an overwhelming majority were with it, and none of them were shot RAW. So I guess I really loved that camera afterall for how much I used it over the A99 and NEX cameras I had at the time.
The NEX 7 was the first and last of its breed. It is one of my favorite cameras of all time for its mix of power, image quality, speed, controls, and overall ergonomics. Still, I would have to do processing to get the look I wanted.
The NEX3/5 were soulless machines that I didn't like for one reason or another, but great on paper.
I would own an X-E1 or X-E2 today given the choice between all
those cameras for still photography. I mean, the best thing I can say for them is my primary stills camera is a X-A1 I bought used for 125 bucks...it doesn't even have the X-Trans sensor. It doesn't have a EVF, it doesn't have alot of things. But it has the look I want, triggers flash, and you can mount the insanely amazing Fuji glass to it. (I'm just using the 27mm).
The video quality definitely sucks, but content is much more important anyways. I shot most of
this series on a X-T1 and some of the previous series on a X-E1...I was a huge noob then but you can see some of what the video looks like. I still am a noob, but I've learned since then for sure.
Things about me:
1. I would have never considered a camera without an EVF (now I don't care as long as the back screen is really good)
2. I wanted ONE camera for stills and audio (Now I think the best choice is one for stills (a Fuji of sorts) and one for video (Panny G7).
Peace.