There may be some discretion involved.....and landing a modern jet safely on one engine is a very doable thing.....but the QRH will say land at nearest suitable airport, as it is definitely a serious incident.
As opinions are free, I'll give you mine......there are very few major incidents like this in one's career, and personally I would take advantage of every resource available, and a mayday call opens lots of doors.
I have flown 3 and 4 engine jets, and our manual clearly said the loss of one engine did not constitute an emergency, ( and you can legally continue to airport chosen by commander- look at BA flight that flew from LAX to London after engine failure on takeoff in 747), I would still declare emergency/mayday and get it back on ground safely.
I have never heard of the Caa/ FAA ever chastising someone because they have declared emergency, but I have seen them question pilots who had a potentially serious problem and failed to declare emmergency.