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It depends on the system. In general aviation piston-engines, oil pressure will provide the variable force that acts against a fixed force such as the centrifugal force provided by fly weights on the propeller blades, or a strong spring.
In some cases, the oil pressure will force the blades towards fine pitch and in some cases the oil pressure will force the blades to wards coarse pitch. In a multi-engine aircraft, it is preferable to have the blades fail toward coarse pitch since that is also towards feather. In many singles, oil pressure will act towards coarse pitch and a strong spring will act towards fine. In the case of a single engine, it is better that the failure of oil pressure in the hub sends the blades to wards fine pitch.
The speeder spring is a different story and it is part of the propeller governor. Its failure would always have the same result - the propeller would move to fully coarse.
Whatever the system in the propeller hub, the speeder spring always opposes the spinning fly weights in the governor. A failure of the speeder spring will 'fool' the governor into believing that the engine is overspeeding because the spinning flyweights will have no resistance. The governor will respond with the action to remedy overspeed. It will try to slow the engine down. That is, it will move the blades towards coarse pitch making the propeller harder to turn.