There are I think 3 different D3's, D3, D3S and D3X, but you probably know that better than I do. What I can say about the D600 as a non-pro user - I've had it for two months, have taken a little over 600 pictures:
- image quality is excellent
- the D600 shines in both low-light and very bright light (shots into the morning sun may need a little processing during the RAW development but the detail is all there, lakes in bright sunlight with a dark building, dark trees and man-high straw-colour shoreline grasses with all details there and no highlights blown. But, a friend who has a D3 says that the D3's low-light capability is even better
- the RAW colours are realistic, the D600 does not exaggerate anything but also doesn't miss anything in terms of colour
- it is very fast, both after power-on and the AF, although with very low contrast or in darkness the AF does need manual help from time to time despite a pretty strong AF help light
- the built-in flash is pretty powerful for a built-in flash
- there was an apparently oily dirt spot on the sensor of my D600 after 365 exposures which could not be removed by the built-in sensor cleaning feature. I wet-cleaned the sensor, and in the process I saw that there were also several (small) white flakes clinging to the mirror tunnel, some of which I could vacuum out, but one or two I could not
- the mirror lockup mechanism stopped working after the first mirror cleaning (mirror came down despite full battery, luckily I was only looking inside with a magnifier at that time, and refused to lock up properly thereafter), and then a few days later suddenly worked again (I hope it remains this way)
- not heavy or bulky at all, I was looking at buying an Olympus OMD because I was worried about this aspect, and now that I have the D600 I can say its size or weight do not bother me in the least
- the camera feels solid enough
- there are enough buttons and wheels for quick adjustments and they are in general ergonomically well positioned, I think as a pro you will be able to make all changes to AF, metering etc. quickly enough
- the AF has different ways of following an object, both in terms of technology and how you do it in terms of pressing a button and which, and these different options to me appear to make sense. There are also plenty of metering options which in my opinion make sense too
- in general the software side options look pretty professional to me, there are plenty for all sorts of scenarios
- you can shoot up to 5 images per second, how many depends on the SD card, but even with a 95 Mbit card for me I couldn't really shoot long series. Also, the D600 has two SD card slots, but they cannot work like a RAID 0, or like saving one image to card one and the next image to card 2 (would be nice for shooting longer series), that seems a bit like a missed opportunity to me
- the menus are in my opinion easy and intuitively to use, and this is my first Nikon
I probably could come up with a few more details, but suffice to say as a summary, there were a few small things, like the spot on the sensor and the mirror lockup issue which should not have happened, but in general this is a great camera. Taking pictures is really fun. The camera during everyday use has so far been reliable, the results were predictable, it is always ready when I need it, easy to use, gives me a lot of options to tweak things but also allows me to point and shoot if I want, takes great pictures - I'm glad I bought it.
I hope this is helpful.