The egg and the chicken...
But AP/FDs are all the same, aren't they?
To maintain a given flight path, they control speed with thrust, and path with pitch (as it taught to IFR pilots: pitch is primary for altitude(or G/s) and power is primary for speed)
To maintain a climb or a descent at fixed power, IFR pilots are taught that pitch is primary for speed, and AP/FD control speed with pitch, while A/THR controls thrust setting.
To maintain a given speed and a given rate of climb or descent, AP/FD use thrust for speed and pitch for rate. Probably the opposite is what is used in light piston airplanes. And probably in this case is when half of the pilots do it one way and the other half the other way.
Maintaining altidude or in an ILS I think we all keep path with pitch, speed with thrust, don't we?