Are each X and each of the Xs interchangeable?
For example, in the following sentence, I would use each of the characters:
Each of the main characters is interesting.
But one could also write the following:
Each main character is interesting.
Instinctively, I prefer the former. Am I right, and if so, is there a written rule favouring the former sentence?
For what it’s worth, Google returns 724,000 entries for each main character, and 11,600,000 results for each of the main characters.
Both are correct. In the first example, each is a pronoun, and in the second, it is an adjective. It is properly used in both cases, and meaning-wise, the two usages are interchangeable in my experience.
As to how common each usage is, I graphed Each character vs. Each of the characters on Ngrams, and Each character appears to be preferred:
However, googling the same thing yields opposite results (131m to 7.26m), so I would tend to conclude merely that both are common. Definitely both are understood, so the use of either should never prove a communication impediment.
To directly answer your last question, no, there is no written authoritative rule favoring either. You may be able to track down subtle nuances between them, but even in that case, both are equally valid within their respective domains.