I own a D800 and I haven't shot a D600. So, I'm not qualified to make a comparison. As to pixels, I'm guessing that in a couple of years, 24 mp or 36 mp is going to seem as a quaint as a computer with 6 gigabytes of ram.
Anyway, after all the negativity surrounding the D800's quality control issues and its reputed propensity to showcase poor technique, I do admit to having felt some anxiety when I took it shooting for the first few times. To my relief, I can report that everything turned out okay. It focuses, the 10-pin connector didn't retreat into the body, the only color shift I see in the LCD is when I forget to lift my sunglasses when I chimp. And after three months, I'm still having plenty of fun. I don't feel like I have to handle the camera with kid gloves. So far I've managed to stay happy shooting landscapes, some fast sports (rugby) and some high iso, high contrast light stuff (dance productions). I loved my D700, and I think the D800 was a rational upgrade both for the improvements and because of its familiar feel in my hands.
And by the way, I have a mid 2010 iMac with 20 GB of RAM, and I'm not feeling the slowdown from the D800 files that I see a lot of complaints about in forums. I mean, yea, maybe a few seconds here and there in Photoshop, and the files download a bit slower into Lightroom. But nothing major.