Does the co-pilot still remain in control of the plane if an engine fails during takeoff?
The operating procedures for the four airlines I worked for (2 commuters and two 747 carriers) all called for the flying pilot (which would be the first officer if it was their leg) to retain control of the airplane until all relevant checklists had been accomplished.

That said, it is, of course, the captain's prerogative to take control at any point. That would, I think, be very unwise to do in the case of an engine failure during takeoff unless the first officer was really screwing up.

The greater workload in the 747 during emergency/abnormal procedures lies with the non-flying pilot and the flight engineer (old 3 man cockpit 747-100s and -200s).

The recommended procedure at my last two airlines was, if the captain was flying at the time of the failure, to hand control to the first officer after all relevant checklists had been completed, to thus enable the captain to give his full attention to how best to proceed.

My personal and observational experience is that there is little difference between captains and first officers at the 747 level insofar as control manipulation during go/no go situations on the runway in simulators. In fact, I could point you to an accident resulting in the total loss of a 747 when the flying pilot was the Captain, and he elected to abort 30 knots after $V_1$, thus insuring the aircraft would leave the runway.