Not a lot of difference. I owned the Nikkor 200mm f/2 AF-S VR for over a decade...I settled on f/2.2 and f/2.5 for almost all of my ultra-shallow DOF shots. At wide-open the DOF is simply so,so narrow at typical closer ranges that one risks having the body out of focus, or the arms out of focus, or the breasts out of focus,etc.,etc..
The thing is this: there is depth of field, and there is selective focus, and there is a closely related thing called
backround blurring. Background blurring is seldom discussed except among the congnescenti. The physically LARGER the lens aperture is, in actual terms, not relative terms, not in f/value, but in HOW LARGE say f/4.5 is, across the hole in the lens, the MORE the background will be blurred. Also, the larger (wider) the lens aperture is in PHYSICAL measurement, the less that diffraction affects sharpness: this is why 4x5 inch film cameras can be shot at f/45 or f/64, and still yield razor-sharp images that do not have diffraction effects.
Because of the way background blurring works on massive lenses, there is a VERY fast degree of defocusing behind the focused distance with the 200mm f/2 and 300mm f/2.8 and 400mm f/2.8 clkass lenses. It's very difficult on a portrait to spot the differences between f/2 and f/2.2 and f/2.5 (which would be wide-open, 1/3 down, 2/3 stop down from wide open).
What it comes down to is that f/1.8 and f/2.0 are only one-third of an f/stop apart, and both are very large apertures, and both produce very shallow DOF, and the degree of difference between the "old 200mm f/1.8" and the new 200mm f/2.0 are very minimal. These massive lenses have BIG holes at all the f/stops, and they create very de-focused AND blurred backgrounds.
Take a VERY careful look at the two photos in this article: one shot with an 85mm lens at f/5.6, the other shot with a 56mm lens at f/5.6. Note that BOTH have the foreground subjects the exact, same size and height in the picture! But notice the diffferent degree of background blurring.
See:
Bokeh and Background Blur Calculator- Bob Atkins Photography
and see also
Bokeh and Background Blur - Bob Atkins Photography for yet another excellent example of how a longer lens, with a physically BIGGER aperture value, creates more background blurring. All three shots of the camera box were done at f/2.8; using 50mm, 85mm,and 135mm lenses.