Germany attempted to upgrade its TypeVIIC Uboats engine performance in late 1940-early 1941 by providing new engine upgrades. There were two German manufacturers who responded to this task: GW and MAN. These manufacturers submitted different ways of supercharging the engine and both proposals were accepted. Germaniawerft engines used a geared supercharger driven from the engine's main drive shaft. On the other hand, Mashinenfabrik-Augsburg-Nurnberg used an exhaust-driven device. By all accounts, the MAN method proved to be superior, adding an extra three knots to the VII for a longer period of time than the additional two knots provided by GW. For all those mechanics out there, is there any obvious reason why the exhaust driven device would be superior than the geared supercharger?
In short: Geared supercharger driven by engine's main shaft uses some of engines output power while exhaust-driven supercharger works for 'free' as it takes its energy from hot exhaust-gases which would otherwise been dumped out. Therefore exhaust-driven supercharger is more economical but I believe geared supercharger driven by engines main shaft is simpler and probably requires less space. Therefore I cant say why exhaust-driven supercharger was superior.
Why not combining both systems? Maybe a Turbo (exhaust driven) is easier to built in on an existing engine in a sub than a geared supercharger?