Kerdok demonstrated a range of surfaces stiffness over which metabolic cost is lowered. http://www.ncbi.nlm.nih.gov/m/pubmed/11796653/ On a individual basis it would seem reasonable that matching the surface frequency to the leg "spring" frequency might be a good place to start.
When looking at running on different surfaces there is often a change in knee angle at contact, with, if memory serves correctly, there is a trend toward the stiffer surface tending to make the person choose a more flexed knee angle.
The quads have to work harder at a more flexed knee angle so there is theoretically an energy advantage to some cushioning in the shoe or the ground.
Certainly, there is an energy cost of having to move a heaver shoe during swing phase.
It looks like there is a trade off between landing efficiency and swing phase efficiency.
This would be consistent with the study Simon pointed out.
The ideal stiffness of the surface and shoe is probably variable across people.
The thesis appears to be about walking, not running.
Walking and running two very different activities when it comes to shoe cushioning and the metabolic cost of the activity.
As far as shoe design for running, the running shoe that has the most cushioned sole with the least shoe mass will probably be best at reducing the metabolic cost of running.
Of course, more material generally means more mass.
However, considering the technological advances in midsole materials over the past decade, running shoes will probably be getting more cushioned (i.e. thicker midsoles) with little to no additional shoe mass in the future.
We have also discussed that walking can be viewed through the spring mass model the same as running. Just the spring is much much stiffer than in running