It's up to you, as captain, to decide whether the situation warrants a Mayday.
What I'd do, and what I suggest to my students that they do, is as follows: after an engine failure, and once everything's under control, assess whether you're able to climb to, or maintain, a safe height. If you are, it's a Pan Pan. If not, it's a Mayday. If there's a fire, it's always a Mayday.
That doesn't mean other twin drivers would do the same. It also doesn't mean I wouldn't change my mind if it happened to me for real. But, probably the most relevant of all, I doubt it would really make any different to the way ATC treat the situation anyway.
FFF
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