Yes, duplicate content is a big issue. Search engines consider it a form of spam and will penalize your sites in terms of ranking, which diminishes your traffic and can be difficult to recover from.
Content is naturally duplicated when shared by people who refer to and comment upon one another. So duplication in this form is legitimate; indeed, it arises spontaneously. Yet it would be unwise to attempt to fake such things by linking to yourself excessively. It's a bit incestuous. And by now so many "black hat" SEOs have attempted such shenanigans that Google is on the alert.
That's all "Thou shalt not" advice. For more positive recommendations, I (or anyone else) would need some details to sink our teeth into.
Both the search engines and users are looking for original and valuable content. I would absolutely put unique and fresh content on both blogs and would avoid duplicating the material. Duplicate content can be an issue as far as search engine rankings as the engines have to make a choice on which website to show.
In the long run unique and valuable content will win the race.