I agree it depends on both the cat and the dog and you can’t predict it. Our cat was 9 years old when we brought home Henry as a puppy. She has always been a bit nervy, so when Henry moved, she ran. Of course as a pup, he chased. Within a few days she had resolutely decamped to live upstairs when the dog is about, and 2 years later is still there! If she had been a different cat and had stood her ground when Henry was a pup rather than enticingly running away, it might have been very different. I’d also be more concerned if the cat was younger, as she has mostly become an indoor cat now. I THINK she goes out at night when Henry is safely in his crate, but I’m not sure. I do know she can tell the time: Henry is generally in bed in his crate by 8:30pm. At 8:35pm the cat will come downstairs and install herself in someone’s lap until bedtime..
When they do cross paths these days they are usually quite calm, but the cat is determined to make it a rare occurrence!