How would duplicate content on two different domains affect our SEO?

Google can rank only one instance of original content from your site to their search results. It will be seen by search engines as duplicate content. If it’s only one page it shouldn’t be a huge problem, however, the pages are likely to not perform as well as they could. The best option would be writing two different blog posts. If that isn’t possible I’d suggest implementing the canonical tag pointing to one of them, depending on which site you want to push or is more important business-wise. This will solve the duplicate content issue but the page with the canonical tag implemented will be disregarded by search engines.