As per my understanding, moving from D7000 to D700, I'll be gaining the following:
More coverage at wide-angle
Ability to achieve shallower DOF (one of the main reasons for this switch)
Larger and brighter viewfinder
Better built and a more rugged body with better weather-sealing
Better AF system
Bigger buffer for continuous shooting
Ability to shoot upto 8 fps using the MB-D10 battery grip
You will have q wider field of view at all focal lengths. What you will also get is faster apertures possible for a given field of view, e.g. a 24mm f/1.4 on a D700 will give you the same field of view as a 15mm lens on a D7000, but the fastest 15mm currently available is two stops slower at f/2.8
Depth of field will be shallower for the same angle of view and same f-stop. Due to the point above depth of field will be much shallower for wide shots.
But I'll also lose the following features:
Video recording (I hardly ever use it)
About 4 MP in resolution
Some focal length at the longer end
Ability to bracket more than 1 EV
95% vs 100% viewfinder (with 0.94x magnification vs 0.74x magnification)
2016-pixel RGB metering sensor vs 1005-pixel RGB sensor
Number of megapixels is not the same as resolution. You'll lose 4MP (which is not that much, basically the D700 images will be 87% of the width and height of the D7000 images) but by virtue of the full frame sensor not requiring as much enlargement to get the images on screen they will suffer less degradation, leading to a greater average level of sharpness. Note corner performance may be slightly less than using FF lenses on the D7000, but centre performance will be much better!
Reach will be reduced, compared to the D7000, so you may have to spend much more on telephotos to get the equivalent field of view, you'll also run into AF limitations fast as maximum apertures get smaller as lenses get longer.
Don't worry too much about the reduciton in viewfinder magnification, as the focussing screen is much larger to start with the viewfinder will still appear larger. Again 100% viewfinder coverage is not a huge deal unless you are exceedingly precise in your compositions!
Dynamic range at base ISO is greater with the D7000 thanks to the newer Sony sensor, but
the D700 will have higher dynamic range in low light, and better low light performance, thanks to the larger sensor.
The D700 is an older and less well spec'ed body in many ways compared to the D7000. However it is full frame, so whether it makes sense to upgrade really comes down to that feature alone.
If you want the field of view a certain prime lens was intended to have, or if you want ultra-shallow DOF or just nice blurred backgrounds at short focal lengths, or if you want the absolute best contrast/sharpness from your images then there is no substitute for a larger sensor.