My cousins' cat Maggie rules the roost at her house. She has 3 rat terrier brother and sisters and they are all terrified of her. They will literally run the other direction if they see Maggie.
On the other hand, Bella will run up to Maggie and keep patting at her until Maggie either slaps her away or nips at her. The first time it happened I about had a heart attack, but Bella waas fine. She waited a few hours and then went back for seconds and nipped at Maggie's tail. Maggie just gave Bella a look of "hullo, I will hurt you". But they just kinda co-exist.
But Maggie is a super great Calico cat. She's more like a dog in some ways. Bella has picked up the way Maggie bats at things with her pawas and she acts like a cat now.
So I say it just depends on the dog and the cat.
