I've used a few of these cameras, I liked the Lumix GF1 ok, We have the Olympus OMD in stock and I've played with it, and it's very comfortable and has a very good EVF.
I own a NEX 7 and really like the tri-nav controls as and the feel of the camera. Other than the accidental video which I've found is quite infrequent now as I've adapted to the camera and the lack of custom setup functions, I've found it one of my favorite cameras. I have a Nikon adaptor so I can use my Nikon Zeiss glass and with the focus peaking feature it's very easy to use. The EVF is very good and in fact it's the only way I take pictures, i never use the LCD anymore when shooting.
The soon to be shipping NEX 6 sounds like a nice camera. Sony has a new intelligent hot shoe, and it's "intelligent" enough to accept standard strobes, (one annoyance of the NEX 7). Instead of two side by side controls there are two stacked controls but I think the top one is a dedicated mode dial instead of a soft dial - most will like that better. It's a lower resolution sensor, but still decent (I think 16mp). All in all it looks like a good camera at a lower price point. The new 16-50 motorized zoom looks like a nice option as it collapses making the camera pretty small. I keep a canon G1x in my backpack so I've always got a semi decent camera with me ... with this lens collapsed the size won't be much larger than the G1x, so the canon might be for sale soon. Lots of other features in the new camera so it's certainly looks intriguing, including improved focusing (which I think can be continuous now), wi-fi (hard to say how useful that will be but has potential)