Never used either, but 24 is significantly wider, f/2.8 significantly faster. Image stabilization is great to have, but may require several shots in my experience with Canon IS.
Say what you will about Ken, but I thought this had a lot of info
I've owned the Tamron 28-75 (I'm assuming this is what you meant) for both Canon and Nikon and currently own the 24-85. The Tamron is the lens to have, no doubt about it. Focus speed is similar, IQ is better, and you get 2.8. The 24-85 is just ok. 24 is wider than 28, but no enough to be an UWA, so for me it is a horse a piece. The VR is nice, but I still feel that the IQ is only ok on the 24-85 VR. I own a D600.
Get the one without the BIM (Built in Motor) if you can. Im not sure about the more recent models but the early ones were slower to focus then with the body driving the lens.
I have a non-BIM 28-75 and it is pretty sharp overall. I have since purchased a Nikon 24-70 though so it is more of a back-up now, though my daughter often borrows it for her D90.
I think for a D600 it would work fine. A D800 though I think would out-resolve it.
I took the Tamron 28-75 on my D600 to Hawaii and it was pretty much the only lens that I used. Great lens on the D600, it was the non built in motor version. Autofocus was quick pictures turned out great. There were just a few times where 28 was not wide enough but I was happy overall with the lens. Ended up upgrading to the Tamron 24-70 just to get a bit wider.
Depends on what I'm using the lens for. That's the WHOLE THING--match the gear to the use. For travel and "general" photography, I'll go with the 24-85 VR. It's more compact, is a bit wider (enough so to be useful), and has VR, something I find useful for "street" shooting and etc. when using a tripod isn't practical. For wedding photography I consider f2.8 to be a "must have." An f2.8 would also give a bit narrower DoF to blur backgrounds for formal portraits, but obviously doesn't matter if you mostly are doing landscapes.
I been using the Tamron 28-75mm on my D700. Fine lens. sharp and nice color. Check the spec.
I think it has less distortion compare with the 24-85mm. The f2.8 definitely comes in handy at times.