The II does refer to the lens version but also in this particular case it refers to "VR II" technology as well. There may be more vibrant colours with the first version if the flaring light source has a different colour than the main lighting on the subject (so you get more colour contrast between main light and shade). The nano-coated "II" version blocks more of the flare out (so shadows are a bit deeper) but you're right it might not make a significant difference in case the sun is in the frame, both lenses will still flare (if the objective is to have no visible flare then this would not be the best lens to choose; the 70-200 FL would be a good choice). But in soft lighting, the nano-coated "II" version of the 200/2 produces more contrasty images wide open than the first version of the lens. The difference largely disappears by f/2.8. There should be side by side images shot by Bjorn at different apertures somewhere in the archives of this forum. It doesn't help to call other people's findings "nonsense" as many of us post the best information we have and try to be very careful about what we say.
Some lenses such as AF 85/1.4 D tend to produce high warm/cold colour contrast in sunny conditions, while the nano-coated 85/1.4G produces a more neutral outcome in such circumstances. This is not necessarily a good or bad situation, both lenses can be used to get desired effects according to situation and taste. I guess it is a generation thing, lenses made in the 1990s behave differently than early 2010's and late 2000's in terms of colour. The Z Nikkors are yet different with perhaps even greater neutrality and high contrast, more "modern". The 85/1.8 Z S and 105/1.4 E tend to produce a bit too high contrast detail on faces for close-ups, whereas lenses like the 85/1.4 D and 105/2 DC can really make people look beautiful in out of the camera images, and the 85/1.4 G is somewhere in between (it's usually nowadays my preference for available light head and shoulders host). The main reason for me to use the newer lenses would be the more precise focusing. (However, back to the topic of the 200/2 both versions focused similarly once fine tuned, but because of the vibrating tripod mount of the first version, it was harder to see where the focus plane was and get the correct fine tune adjustment made).