From their interviews:
Leliana:
[SC]: She has a healthy respect for Cassandra, even if she doesn’t always agree with her. Ultimately, their goals align, and they’ll work together for what they believe is the greater good. It’s a little like Mom and Dad quarrelling behind closed doors, but presenting a united front to the kids. Same goes for Cullen.
Cullen:
[BB]: Cullen has a lot of respect for his fellow advisors. Of course, that doesn't mean they always get along. For example, Cullen is a practical person who appreciates a straightforward, honest approach. Leliana, who has worked behind the scenes for the Divine for years, won't come at a problem the same way.
Josephine:
[SF]: She has a good relationship with Leliana. They’re old acquaintances, and they both know the other is very good at what they do. That said, I think it is a relief for them to see: “Oh, our work styles mesh after all. Phew!” That’s not to say they always agree with each other, but they’re a good team.
Meanwhile, while Josephine and Cullen respect each other, Josephine would always rather work towards a diplomatic solution while Cullen doesn’t always think it’s the practical choice. Josephine can get impatient with that attitude and the clash in their philosophies.