Compared to some of the other dynamics in the Harry Potter, Sirius and Bellatrix's was rarely in direct spotlight, whether in the books or the movies. They have, however, one of the most interesting and intriguingly unappreciated relationships in the series.
First of all, their parallels -- they were both prisoners of Azkaban for over ten years, making them both sullen, depressed, haunted individuals who are overly familiar with battling for sanity and hope against the dementor's oppression. The difference? Sirius pulled through, Bella gave in. Still, even if Sirius was strong enough to avoid a complete mental breakdown, you can still see that crazed, rabid look in his eye sometimes. They both held onto hope to keep them going-- Sirius to the hope that he would escape and find Harry, and Bella to the hope that Voldemort would return and save her. They're both Blacks, pureblood elitists by birth, and quite honestly they both probably would have stayed that way if Sirius had been sorted into Slytherin. And they are a nearly even match in a duel.