The short answer is that medium is better ... in *all* circumstances.
Well ... if you shoot bright light all the time and very fine, but very high contrast details ... and you like to pixel peep at 100% ... then shooting HR mode might satisfy you now and again.
But for general purpose shooting without requiring of constant thought or the use of the battery-eating EXR AUTO mode, just shoot P mode with M size.
My test today is a pair of shots of a stack of books I have to file at some point ... I focused on the label and title of the Nelson DeMille book Wild Fire (good thriller by the way.)
I cropped the focus area first, since it is bright and should be quite close between the two ... I found in fact that the labels and text are more readable on the 5mp image that was upsized to 10mp than it was on the 10mp native image.
Those who have read my thoughts on this in the past know that I consider the HR mode to be evil ... it shows weird edge artifacts, no doubt caused be a combination of the rotated SCCD matrix, and the strange pixel-paired EXR arrangement of the colors. Between these two, they are performing some ugly math to get a simple image matrix. With the binned mode, we no longer have the pixel pairs, so we are back to the original SCCD demosaic algorithm, which we know works very well.
Added to the strange bayer mask, we have Fuji's selective noise reduction. At 10mp, the details are very fine, yet there are a lot of weird artifacts that no doubt look like noise to the jpeg engine. So Fuji tries to smooth the flat areas, which inevitably damages edges of letters etc. This is *very* obvious in these images.
Starting with the crops ...
Remember to click on these images to get the larger 800px versions. The crops show just how much cleaner the edges appear. Start with the words "Pix Reg." on the circular label. Perfectly clear on the upsized image, but the x is destroyed by edge artifacts in the 10mp native image.
Next, have a look at the spine of the book "Follow the Stars Home" by Luanne Rice, just below the book by Anne McCaffery and Jodie Lynn Nye (The Death of Sleep.) The title is discernible on the 5mp image while it is simply mush on the 10mp image.
The next crop down is the spine of "Light: Science and Magic", a superb book on artificial lighting, especially of difficult subjects like glass and mirrors. The word Light on the upsized 5mp image is crisp and clear while the 10mp images shows it weakly with a lot of grain. The fine grain has fooled some people to declare that edge definition is much better in 10mp mode ... this, of course, is obviously not true. In some very few cases, the 10mp mode can resolve a bit more high contrast detail, but there is *always* the price of chroma noise and edge artifacts along with smoothing of any low contrast details.
The final crop is the Harry Potter spine ... it shows poor definition on the author's name and it shows a lot of nasty chroma noise on the main part of the spine. The noise on the 5mp mode is mainly luminance grain ... a much more pleasant form of noise.
What I find really interesting is how these issues are subtly visible even at tiny web sizes. Showing the upsized image first:
It looks pretty good. Everything is crisp and clear. The 10mp image looks superficially similar ...
But now take a look at some of the crop areas. Also look at the title of the Stephen King book "The Stand" ... you will see that the title stands out clearly against the red background with the 5mp image, which blending back in (the result I believe of NR and edge artifacts combined) to make it harder to read on the 10mp image ...
I see no reason to *ever* shoot 10mp on the F70EXR or 12mp on the F200EXR ... every time I see a pair of images from these cams in the two sizes, the issues with edges and low contrast detail stick out like a sore thumb.
I realize that many people don't see this ... but train yourself to look for this kind oft thing ... it won't be long before you see the kind of improvements that make a big difference in your image's ability to convey 3 dimensions.