What should we do in these situations?
Nothing. They're two different sites with different (but overlapping) audiences. In this specific situation, the exact same question (and its answers!) would be appropriate on both sites, but there'll be plenty of cases where that won't be true, where the needs of a brewer and an enthusiast overlap but don't align perfectly.
Generally-speaking, Stack Exchange sites are expected to stand on their own, catering to their own communities and being a bit jealous of their questions - there's no such thing as a cross-site duplicate.
That said, there are two things worth keeping in mind, particularly early on:
If you're pulling relevant information from a different site, don't forget to attribute it properly. Ideally, there'll be cross-links between sites with related topics, with overlapping expertise aiding readers on both.
Don't post identical questions on both sites, and be very careful about re-posting questions that've already been asked elsewhere. It's important that we establish a clear role for this site during the private and early public betas; if the questions here are too close to what's available elsewhere, it'll make it harder for future members to recognize what is and isn't on-topic. Focus on identifying areas where the good folks here weren't being served, and make sure the answers they're receiving are fresh draughts.