It is a very hard question to answer. I have been agonising over this choice for the last 3 months. When I finally went to the store, I spent one hour playing with both cameras and still I could not decide. In the end, I went for the D800. It was an emotional decision, not a practical one. I was afraid that if I go with the cheaper camera, the thought that I could had a better camera would nag me all the time.
There is a view that D800 is a specialised camera, more suitable for studio work or landscape shooting and when you need to print very large. The D600 is a more general purpose camera and is easier to handle in common casual shooting situations. Several of the well respected pros recommend D600 over D800 (Scott Kelby, Moose Peterson, Nasim Mansurov, Ming), although all of them have D800 and love it. But they are pros and they also have D4 when the speed is needed.
In my view, you should not make your decision based on the reports of potential problems with both cameras, when I went to the store, they had both cameras with serial numbers 6xxxxx, and I am pretty sure that Nikon has solved all the reported issues by now. If you get a faulty product, Nikon will fix it.
As to your other questions, both fps and noise performance are quite close, the difference in file size is also not huge. So, if you ignore megapixels and some handling differences, both cameras are almost the same and will give you comparable results in 90% of the shooting situations. That is why in my view, this choice is not rational one.
Sorry, I probably has not given you a simple answer. The most important thing is that you will be very happy with either camera, they are both state of the art. So, make a choice and move on to shooting!!!