Exactly how much control does an Airbus Pilot have over the plane opposed to a Boeing Pilot?

the amount of 'control' is effectively the same although in the airbus if the captain puts in a control and the first officer puts in an opposite control the aircraft goes abit funny as it is a pure fly by wire aircraft. on a boeing (say 777 for example) which are not 100% fly by wire (you still need to manually trim the aircraft to hold a certain attitude whereas in an airbus the trim is automatic), moving one control will move the other control as well. boeing kept this feature so that the non-flying pilot (pilot monitoring or PM) can see what the pilot flying is doing with the controls. also the 777 has mechanical cables attached in the unlikely event of a total hydraulics failure, for example spoilers 4 and 11 are mechanically linked to the control column.