DX to FX
My path was D70s to D200 to D300 to D700 to D800e. Enjoyed them all. Still have the last four.
Big increase in IQ? No, unless you are a) shooing in low light, handheld, and/or b) printing really big or cropping a lot and need a lot more pixels and go for a 24-36mp camera.
When I added the D700 to my mix, it quickly became my go-to/everything camera, or everything-but-wildlife. The D700 can do everything the D300 can do, and more, except put more pixesl on a too-distant subject.
Here's where I saw visible improvements in IQ: high iso, 14-bit shooting speed, and dynamic range. The cameras are pretty much equal everywhere else. And of course the FX camera has a width advantage (when coupled with my 14-24), while the D300 has the crop reach advantage.
I always felt like I could shoot the D300 up to ISO 800 or so without worrying much about things. Once past ISO 1000, I did have to expose carefully and expect noise in the images and/or reduction in sharpness. I tended to be very worried about shooting over ISO 2000, though I've got some excellent results at ISO 2000 where the dynamic range of the scene wasn't very extensive.
Basically the D300 topped out at ISO 1600 for me while the D700 topped out at about 3200. Both can go higher, with post processing really needed.
14-bit. Can't say for sure i can see a difference, but the D300 can't shoot fast in 14-bit mode. It's limited to 2.5fps, plus the shutter lag is almost doubled. I leave it at 12-bit so I can shoot at 8fps with the grip. The D700 stays are 14-bit.
The D700 has more dynamic range. At least that is my assumption. It clearly has more headroom for pulling down highlights, and more shadow room for pulling up those. Skies look 'smoother'. The whole output just looks 'smoother'.
Where would a D700 help you? Probably in those rooms where you haven't got the time or ability to light up every shadow, and/or where you have to handhold at ISO values over 1000. Plus, if you get a 14-24, it will be really, really wide. You probably won't like the keystoning effect though - it won't be generally flattering to the architecture. A PCE sounds more suitable, and 24mm is often wide enough.
As others have said though, the newer DX sensors are clearly better than the D700, plus have more pixels. It doesn't sound like you need the features of the semipro bodies (D300/D700/D800) either, especially with a PCE lens where you're going to be working slow and probably from a tripod. Simpler to get a D3300 or D5200 or D7100 - your DX lenses still work, and there will be a noticeable IQ impact.