For Eu Ops – CS 25/FAR25 aircraft, the AFM climb performance is normally based on V2, thus fly V2.
However, if the turn requires an angle of bank greater than 15 deg, for a lower radius turn, then a higher speed may be specified. If required, this should be in the procedure; also check for any wind limits which might affect the assumed ground track.
If the engine failure occurs at a speed above V2, then maintaining that speed should give a better performance profile, but check the procedure detail and assumptions.
Also check, up to what point the engine failure is assumed after takeoff such that the procedure applies, i.e. after what point do you continue with a normal departure.
IMHO the Captain who flies a speed other than V2 is mistaken in his knowledge of aircraft performance and aerodynamics. Entering a turn at V2, the aircraft would be expected to fly at a lower attitude than for wings-level flight, thus adjust accordingly. If, in error, wings level attitude is maintained in a turn then speed will reduce; do not fly below V2.
Maintain V2 or the speed specified in the procedure.