"... US stuff is pin point accurate even on the move, the Germans even touch the gas pedal the hit circle gets as big as a house ..."
Stabilized Guns for Yanks' Tanks
Germans didnt used them ever in any of their vehicles except for rumors about the Panther II geting them. But its not even sure if there has been ever a runing prototype.
While those stabiliziations in WW2 have been not even close to what they are today ~ an abrahams has no issue to hit a target 2000meters away while driving full speed, they could give you some advantage while stoping and starting.
Though I havnt noticed much difference in accuracy between guns except for the super long range weapons like the 90mm or 88mm.