Don't you love this forum for advise? I find the folks here to be very informative, practical, and thoughtful in their replies. I'll endeavor to follow suit.
To me, the difference in megapixels between the D600 (24) and D800 (36) can be an advantage or a disadvantage. For my personal use, I find my new D7000 (16MP) already creates files in excess of what I'd need to print, so it's plenty.
I know storage is cheap and fast computers with adequate memory aren't bank-breakers anymore, but bigger files mean more storage space and can certainly take longer to post-process.
As far as other features go, I'm not a sports shooter, so being able to go to 1/8000 shutter speed instead of 1/4000 is a non-issue (aren't both of those numbers mind-blowing, by the way?)
You do get more AF points with the D800, but 39 (what the D600 offers) is a lot to begin with.
The price difference between the two seems to be around $900, and personally, if I were spending my own money, I'd rather have the D600 and spend the rest on glass.
Either way, you'll hardly be disappointed with either camera, but I think taking a good look at what the extra $$$ buys you and deciding whether those features and specs are actually useful in the type of shooting you do is time well spent.