I don't think there is a Senju relation to all jinchuurikis, but yeah, rather the amount of chakra and how well they control it. Bee was good because he was able to match his with A, who's chakras have been compared to a bijuu, he also was the cousin of the previous jinchuuriki. Gaara was kind of the same way, he was the only one out of him and his two siblings that was compatible. The rest we really don't know that much about. The fourth Mizukage was supposedly a perfect jinchuuriki, I'm sure there is something special about his lineage. Then there is the Kin/Gin brothers who had special genetics, enough to survive in the belly of the Kyuubi by eating its flesh, then came out with some of its power.