RAW File NEF/DNG - PS CS6 vs PS CC

The difference will be in the default processing only in ACR and not caused by any change from NEF to DNG.  CC has the latest and greatest image processing goodies as you would expect, and they do make changes / improvements to the image.  Nothing in Adobe software is static, but if you had settings saved in ACR CS6 they can be used in CC to keep a similar look.  

You've been listening to Capture One marketing - that's their line. It's utter nonsense, they just refuse to fully support DNG because it doesn't fit with their "secret sauce", "magic" etc marketing. There's nothing magic about it, but if they supported DNG the bottom would fall out from their carefully constructed image.

No, there is no inherent difference between DNG and NEF. They are just different containers for the same data, which is, simply, a dump from the camera sensor. The both contain the same sensor data and the results will be identical.

It's difficult to say. But I suspect that it would look different because Photoshop CC and the updated Camera Raw would have different defaults for the camera and those defaults would utilize the new settings available in the later version of Camera Raw, not to forget at least one new process version. But, of course, that will be after that camera model is eventually supported by Photoshop CC and Camera Raw.