I went from the D80 to the D300 to the D800, so I had a pitstop in between that might impact my impressions. However, my wife kept the D80 and I still help with it occasionally (I let the D300 go, she wouldn't use it).
When I go back to the D80 the thing I notice first is size. I had the D80 with the 18-200, and at the time I thought it was nicely large. Now with FX lenses (e.g. a 24-70 or 70-200) on the larger D800, the D80 feels a bit like a point and shoot.
I mention this as if you are deciding what to get next, be sure that larger is OK. If you move to the D800, over time everything gets a bit larger - the FX lenses because they are FX, plus you may go for higher quality (heavier) and faster (larger), not just the bigger camera.
I LIKE the large. I now can hardly use the D80, I had forgotten how hard it was to find the controls while your eye is to the viewfinder. On the D800 and D4, I rarely look, there's plenty of room between controls, and I adjust them easily. But my wife hates it, she wouldn't take the better D300 because it was larger, and the D800 is a bit larger still.
I think the whole world wonders if Nikon will continue the DX line with more semi-pro gear like a D400, but perhaps even more importantly with more DX glass. Right now if you want fast, high-quality glass there's not much choice in DX (obviously FX glass will work on the DX, but you loose the size/weight benefit). I personally do not see them ever investing heavily in DX glass, just the consumer grade. Those willing to pay $2000+ for a lens probably also have (or know they might get) FX. So I think if you envision getting high quality glass over time, it's going to be FX regardless. One opinion.
I love the D800. I highly recommend it. I would never go back to DX; the FX pro glass is just amazing in quality, and if you are going to pay the weight penalty on the lens the camera size is largely irrelevant. But the D7x00 also have really great sensors, in a smaller form factor, if you decide to stay DX.
If you are at all inclined to look very closely at your shots, go for the better glass. I don't have either the 28-300 or 24-120, but understand the latter is better and a good choice. Depending on your budget, you might also consider a 24-70/2.8 plus a 80-400. That gives you a wonderful, very fast, very sharp lens for short walk-around, and a 5:1 zoom that is also nicely sharp (but not fast). The F2.8 glass would be more important if you do indoor and low light work; if you don't do much of that (without flash), the 24-120/F4 is lighter, cheaper and might obviate the need for a telephoto.
Another option is a wide range zoom (maybe even the 28-300) then get a couple of primes for when you want the most in quality, e.g. a 50/1.8 and 85/1.8 are collectively not very expensive and are very sharp and flexible with low light.
Rumors say a new D610 is coming, but I have heard nothing about a D800 followup soon. And trying to guess what's next and time the purchase is a bit like timing the stock market.