I am a native UK English speaker and have spent a few minutes trying to figure out the difference between the two phrasings. In an informal situation, such as a simple conversation I don't think we would expend effort to select one or the other; both imply a very positive motivation.
If we were delivering a formal speech or were producing a written document we might note that
is plural, implying that there were more than one reasons for the action. Whereas
nicest of reasons
allows for there being a single motivation. I do think that the phrase does not exclude there being multiple nicest of reasons.
I suspect that the we would actually select one phrase or the other based on our sense of style and rhythm. To my ears "nicest of reasons" seems, um, nicer. I had thought it was actually more idiomatic too, but I can find no evidence for that; "nicest of reasons" seems not be found by Google's ngram.