If you go by Jon Speed's books, the A (English style) and M models came after the B and S styles. Going by interwar German catalogs, the model S was the standard offering in Germany, while the M was predominantly made for export, available on special order only, just like the A and "African model" types. So you see S types much more often than M types here in Germany, though all Mauser, Oberndorf, prewar commercial rifles are rare here. IMHO there were many more S Stutzen made originally than the M type export model. But then came 1945 and aftermaths. Note, Jon wrote:
"It is not always easy to locate a REALLY GOOD EXAMPLE of the Model S"
Survival rate is the cause here. While most Mausers, exported pre-WW2 to Britain, USA, Scandinavia and elsewhere survived the ravages of time quite unmolested, gun ownership in Germany was a crime, punishable by death, in Germany from 1945 -1950. All firearms had to be surrendred immediately to the Allies. Most guns were destroyed, some "liberated" and now found in the USA and elsewhere. Guns that remained in Germany were hidden away in the most unlikely places with often adverse storage conditions. I even know some guns that were buried in a grave, some inches above a coffin. When gun ownership became more or less legal five years later, such hidden guns were retrieved from hideouts. If not rusted and rotten beyond repair, they were repaired to "useable" by some means, many restocked or rebarreled with an ex-miltary barrel. Sometimes the scopes had survived under better storage conditions and could be put back on the rifles. Others were mounted again with any old scope available and makeshift claw mounts. The few rifles that survived the five post-war years in decent shape were now used for 60 years, often remounted with "modern" scopes and mounts. Remember, the true commercial Mausers were appreciated here just as usable rifles, until American books by Olson, Womack and Speed appeared. So most commercial Mausers you find now in Germany are either quite sorry examples with rust pitting and discolored stocks, refinished post-war, or reimports from other countries, often Sweden.
In all, Germany is likely the worst place to look for a decent pre-war Mauser rifle, especially a M or A. As customers in many other countries preferred the looks of the more expensive M type over the S, there may be the false impression that the M type is more frequent than the S one.