The claim about asphalt being "softer" than concrete is absolutely correct. The problem is that some people here [intentionally] insist on misinterpreting what is claimed.

The claim does not refer to the physical properties of the material itself. It refers to the nature of the contact between the runners shoe sole and the surface. In this case the word "asphalt" is actually a reference to the typical pavement surface of a typical road. As you all know, asphalt-paved surfaces are usually not very smooth. They look like rough sandpaper, magnified. The surface has lots of small "peaks" and "valleys". Meanwhile, concrete-paved surfaces are typically smooth and texture-less.

This is exactly what creates that feeling of "softness" often associated with asphalt-paved surfaces. As the runner plants its foot on the road, the runner's shoe first comes in contact with the "peaks" on the rough asphalt surface. At this point the shoe already begins to support the runner. As the sole pressure increases, the soft sole material conforms to the peaks in the road surface and continues to flow downward into the "valleys" around those peaks. As more and more of the sole surface comes in contact with the uneven road surface, the support provided by the shoe increases untill it becomes sufficient to counteract the full weight of the runner. The important characteristic of this process is that because of the typically uneven surface of the asphalt, the supporting force increases gradually (as the sole material "wraps" around the peaks and "flows" into the valleys). This is what creates the very real effect of additional softness (on top of the softness of the sole itself).

The concrete-paved surfaces are virtually always almost perfectly smooth. On a smooth non-giving surface the only softness you can feel is the softness of the shoe sole. There's no gradual "flowing" effect described above. For this reason, concrete surfaces feel hard, compared to asphalt surfaces.

So, again, it is not about the properties of the material itself. It is about the properties of the typical surface profile produced by these materials under the typical modern road-paving technology. If you intentionally make a rough/textured concrete surface (i.e. simulate typical asphalt surface with concrete) and compare it with a very smooth asphalt surface, you might discover that the concrete in this case feels softer than asphalt.

I was considering proposing exactly that as a possible explanation.
If true, then texturing concrete could be a solution to make concrete as acceptable as asphalt.
Of course I doubt this would matter to runners (such as myself) who land on the forefoot.

Completely the solution. Obviously we should advocate only our own belief system, or yours.

Great theory, and interesting reading, but I simply can't believe it's enough difference to notice in a blind test. Outside of randomness, I don't believe you could ever get a statistical percentage of runner to choose their surface correctly in a blind test