Why different speeds?
There have been many good comments on the speed to fly. I would like to offer another for the aircraft I fly.
For the 767-300ER that I fly, I am not able to provide engine anti-ice for the inop engine.
This means if I am flying at Vmo at FL 210 in the clouds, I might be adding a bit of complexity to the event (increasing ice accumulation). If I am able to remain on-top of the clouds at FL270 by flying the FMS engine out speed, then I would certainly take that as an option.