Yes, the specs are very close. And if you really needed the extra resolution, the D800 has it.
http://www.dpreview.com/products/compare/side-by-side?products=nikon_d600&products=nikon_d800
dpreview.com does list some spec differences, D600 stated first, (D800 stated in parentheses):
24.3MP Full-frame CMOS sensor (compared to 36.3MP CMOS)
10.5MP DX-format crop mode (compared to 15.3MP)
39-point AF system with 9 cross-type AF points (compared to 51-points, with 15 cross-type)
Autofocus sensitivity down to -1EV (compared to -2EV)
Maximum 5.5fps continuous shooting in FX mode (compared to 4fps in FX mode)
2,016-pixel RGB TTL exposure metering sensor (compared to 91,000 pixels)
2x SD slots (compared to CF+SD)
No 'Power Aperture' aperture control during movie shooting (offered by D800 using Fn + Preview buttons)
Shutter rated to 150,000 cycles (compared to 200,000 cycles)
Magnesium-alloy top and rear covers only (D800 has full mag-alloy chassis except flash housing)
USB 2.0 interface (compared to USB 3.0)
I suggest reading the D600 review on dpreview.com as it contrasts the D600 with the D800 at various points throughout.
http://www.dpreview.com/reviews/nikon-d600/