Just like in English, there are many ways to pronounce Latin.
Would you say that British pronunciation is correct and American is wrong?
Any valid pronunciation will do, but the best choice depends on context.
If you are singing a song from 18th century Germany, it is most appropriate to sing with with the corresponding pronunciation.
If you are reading Catullus out loud, it is good style to use pronunciation of his time and place.
There is no single ecclesiastic Latin pronunciation — pronunciation depends on time and location.
Choice of pronunciation may also depend on audience.
If you speak Latin to a Finn, you will probably be better off with a classical pronunciation since that is what is taught in Finland.
(And if you want to impress your Latin-speaking friends, note that a slightly older version of pronunciation is used in Turku than in the rest of Finland.)
It can be difficult to adjust pronunciation to different situations, and sometimes I think it's better not to try to adjust.
If the contextually most appropriate pronunciation is too difficult for you or you cannot follow it consistently, do as you do best.
The song you mention has medieval origin and I find it appropriate to sing it as its writer would have sung it.
If I were to sing it myself, I would nevertheless do it classically, just because that feels most natural to me.