Are you about to crash?
Yes, the commander gets to decide what state of operations is notified - either, I am in a state of operations that is currently safe but requires expedited handling to minimise the exposure to further risk (Pan Pan), or, I am in immediate danger of losing control of my aircraft or the situation (mayday). It is possible that an engine failure may lead to the second operational state, but in most situations it should not - if it did, then the whole certification bases and training requirements would be based on a false premise.
I think that you carefully analyse what situation you face and make an appropriate and relevant call. I have severe reservations about this theory that a Mayday call is the universal call of first choice - I think that approach is as silly as that where people refuse to declare their situation at all!