I was just thinking about this a bit more and we should be careful when comparing StuGs with tanks since the Sturmgeschutz units were attached to the artillery rather than panzer branch of the army. As such unit makeup differed.
Excerpt from :
http://www.historyofwar.org/articles/weapons_StuG_III.html
"At first the StuG was used to equip independent Sturmartillerie-Abteilung (assault gun detachments). These each contained three gun batteries, each with six StuGs divided into three platoons, giving each detachment eighteen StuGs. Later on the battery commanders were also given a StuG, bringing the theoretical total up to twenty-one. These batteries and detachments were not to be permanently attached to any particular division, but would be attached to unit for specific operations.
This system took some time to put in place. At the start of the German offensive in the west in May 1940 the StuG was in use with Sturmartillerie Batteries 640, 659, 660 and 665, and only twenty four vehicles had entered service by the end of May. One of these batteries then became part of the infantry regiment “Grossdeutschland” (the predecessor of the more famous infantry division of the same name).
The detachments began to take form in August 1940. By January 1942 a total of 18 Sturmgeschütz-Abteilungs had been formed (the name changed in February 1941), while three batteries had been formed as part of the SS Divisions “Das Reich”, “Totenkopf” and “Wiking”. This was the start of a process that saw the StuG spread out from the independent detachments to become an integrated part of a very large number of divisions and other units. "