parkfell,
Important here to differentiate between the priority state (MAYDAY v PAN) and any emergency response that the tower will call to meet the aircraft. They are two different matters. ATC can put on a Full Emergency response for what the flight crew might not deem an emergency (engine failure, One of four hydraulic systems failed, etc). Conversely, ATC might not call any response at all for a MAYDAY.
It all depends on the issue at hand.
MAYDAY v PAN is only used by ATC to determine the priority level of that flight among the other flights being dealt with at that time. We then use the detail of the problem to determine the emergency response.