Both are really incredible movies, and I'd also highly recommend them. "How To Survive A Plague" is pretty great too (it even features everyone's favorite NIH official, Anthony Fauci!).

One thing worth being aware of with "And The Band Played On": it's quite old, and science advanced a lot after the book it's based on was written, so it's sometimes factually inaccurate (Gaetan Dugas didn't personally cause the pandemic, and the incubation period is longer than they thought then). It's not a work of history or a documentary, but it makes for fascinating viewing precisely because it was made so close to the events that the story it tells is not neat and polished with the benefit of decades of hindsight and narrative shaping. It's chaotic and emotional and raw and authentic and, inevitably, sometimes wrong about stuff that wasn't known then.