I am not an expert in this area, but my understanding was that while the Iliad is not "Greek drama" per se, the job of the Greek rhapsode was considerably ritualized - i.e. theatrical - while Beowulf's origins are a little more mysterious, but comparable e.g. Icelandic sagas were definitely not so.
The opening invocations - to the muses vs. compatriots - point at very different contexts the stories pretend to be told in, even if that too was part of the fiction, now or then.
The opening invocations - to the muses vs. compatriots - point at very different contexts the stories pretend to be told in, even if that too was part of the fiction, now or then.