After testing nearly every setting (concerning image quality) in P- and the EXR-modes, I came to the following conclusion:
P-mode 12 MP pictures offer hardly any advantage over 6 MP pictures, except in some few cases (i. e. fine high contrast detail).
The DR-technology (reading out 1/2 of the pixels after 1/2 of the exposure time to increase dynamic range) works in P-mode when image size is set to 6 MP: P-mode 6 MP offers DR 400% @ ISO 100, which is not possible with 12 MP or in HR mode.
The SN-technology (combining pixels for lower noise) does NOT work in P-mode with 6 MP. P-mode 6 MP ISO 400 shots show more chroma noise than SN-mode ISO 400 shots. P-mode 6 MP ISO 1600 shots are as ugly as 12 MP ISO 1600 shots. I wonder why this is?
DR 400% offers only slightly lower dynamic range than DR 800%, but produces cleaner images due to its using ISO 100. DR 800% is possible only with ISO 200, which results in additional luminance noise, making the images look less crips when viewed at 100%.
Thus, I have to revise my preferred modes of operation. I now use my F200EXR almost exclusively with 6 MP (12 MP also creates strange artifacts and images look soft, like interpolated 6 MP pictures) in P-mode with DR set to 400%. If necessary (for example for pictures taken outside in sunlight), I switch to A-mode, so I can force the camera to use the greater aperture (the camera tends to use the smaller aperture when this results in long exposure times and possible blurring of the image).
Up to 400 ISO P- (or A-)mode produces VERY clean images. For 800 and 1600 I use the SN mode, with additional cleaning of the quite strong luminance noise in 1600 ISO shot with NeatImage (ISO 800 needs no cleaning, imho).
The camera has some flaws. One of them is the already mentioned tendency of the P-mode (and other automated settings) to use the smaller aperture when this would result in unnecessary long exposure times. This is why I often use A-mode for outdoor pics. Another flaw is that the image stabilization does not necessarily stabilize the picture, but start to work when in fact it isn't needed, resulting in blurred images. As suggested by another user
here, I will try and manually activate IS only when shooting with long exposure times.
I have yet to find out in what situations the 12 MP setting DOES offer a resolution priorty over 6 MP. One example where 6 MP produces clearly better result was taking a picture of a white towel. The 12 MP picture looked soft and couldn't accurately reproduce the low contrast detail of the motive, whereas the 6 MP picture (taken in P-mode ISO 100 DR 400%) was crisp and sharp and showed every detail. The other case was high contrast detail (written text) shot form a greater distance. In the 12 MP picture I could still make out most of the letters, whereas in the 6 MP picture I could hardly differentiate them anymore.