Comfort, P., Allen, M., & Graham-Smith, P., (2011). Kinetic Comparisons During Variations of the Power Clean. Journal of Strength & Conditioning Research, Volume 25 (number 12) 3269-3273.
This article in the most recent NSCA journal discusses two basic variants of the power clean exercise. The clean is an excellent exercise for training power production of the lower body. It's already assumed that the power version is preferable for sports training for it's specificity. This study examines the differences between starting positions: on the ground, the hang position and mid-thigh. The study also compares the clean pull from mid-thigh.
The study found that the mid-thigh start position produced the highest force (ground reaction force (GRF)), highest rate of force production (RFD) and highest power (P). The clean and pull produced similar forces. For the purposes of sports training, and especially the incredibly quick movements of combat, these characteristics are some of the most important.
That the force characteristics are highest for the mid-thigh start is not surprising given the mechanics. Regardless of the start position the bar has to be brought to the same end position. Producing sufficient force for this with a smaller movement requires the acceleration to be higher. And so RFD and Power are higher.
The conclusion is that, for sports and combat training, the mid-thigh start position best suits the the strength objectives.