Actually, when I swapped my Sony NEX 5R system for the Olympus I now have, I was seriously considering the Sony NEX 6. It solved several of the issues I had with the 5R and is a very good all around camera, much better than the 3N, which is an entry-level model. The lack of weather resistance and limited lens options are what swayed me to switch away from NEX completely. The wi-fi and touch screen were never an issue; I never used them. If those lacks don't matter to you, I'd suggest strong consideration of the NEX 6.

Of the requirements you mentioned, (1) any of the cameras you are considering will help with the shutter lag you get with a point and shoot. (2) In general, the newer and larger sensors will give improved high ISO capability for low light shooting, so again, almost any (except the Nikon) will show marked improvement over your P&S. I shot a stage production with my NEX at ISO 1600 - 3200 with quite acceptable results. (3) The blurring of the background (called bokeh) is a function of sensor size, wide aperture, background separation and some technique. Shoot anything at f/2.8 or less (wider is better) with a decent sensor and you will blur the background. The ability to get those wide apertures is in the lens rather than the camera body. Couple a good, reasonable sensor with a fast, wide-aperture lens and bokeh becomes fairly simple to achieve. The quality of the bokeh is another matter and generally is a function of lens quality. Discussion of bokeh quality is way beyond the scope of this thread.

Unfortunately, most kit lenses included with almost every camera system are not very fast. To really get good bokeh, you are going to have to look at additional lenses beyond what comes with the camera.

One thing that hasn't really been mentioned. None of the cameras being discussed in this thread is really "pocket-able." With lens attached, even the relatively flat Sony NEXes and the Olympus PENs aren't going to fit in a shirt pocket. They are much smaller and lighter than a DSLR but still will require some sort of case or carry system.

I would recommend going into a good dealer and handling the different choices you are considering. Sometimes just how a camera fits your hand and eye is as important as the feature set. As an example, the Oly I am using now has really tiny control buttons which would be difficult for someone with large, thick hands. It is still a great camera but that is a consideration.