I'm not a supercharger expert.... but from what i recall, the physical design of the rotrex is centrifugal - meaning the faster the airflow, the more rpm of the blower = more power. its essentially a turbo on the inlet side.
However, the Eaten is a 'screw' type, which (depending on its design) means it has a very definitive 'peak', where it will produce max airflow, and can then become a restriction if engine RPM airflow requirements exceeds this.
But, ive probably picked up an apple and a pear there, and tried to compare. Im an NA man, not a FI! lol.
What im getting at, is i was of the belive Eaten was designed for low-mid RPM power (mainly because of design limitations at high rpm). Rotrex were for high RPM, 'replacing' turbos as they do not suffer from the same high intake temperatures design flaw.
As for gearboxes - There was a chap at the last dyno i was at that that had a 6-speed fitted to his F/TF. Im SURE i heard the word Toyota mentioned in the conversation... although i was only evesdropping, and didnt get the whole thing.