I agree that cat's are more dangerous than dogs, dogs are loud and let you know where you are as cats are stealthy and sneaky,(which is why I close my door as fast as possible,) I always make sure that my heavy door is closed all the way. Cats also see birds as prey, and dogs might see a bird as a toy. You can train your dog for accidental situations (bird gets out while accidentally while dog is out) so that you can lead your dog out of the room as fast as possible, while a cat you can't say, "stay," or "come", they might just go running after your bird with no regard to you trying to get your bird to saftey.I now only have the 1 dog but the rules in my house have always been that when birds are out of cages flying about the dog is locked outside or in another room.
I’m now the only one who is ever allowed to let the dog in or out so there’s never any mistakes with that (anymore), things were very stressful when everyone else was also letting dogs/cats into and out of certain rooms and I did have a few very scary moments- other people are honestly the biggest problem for me in multi pet households.
I never ever have birds and the dog free roaming in the same room as it’s just not safe for the birds- cats I feel are even more of a danger.
The stray cats watching my birds from quite some distance away and through a window cause my birds serious stress- it’s to the degree that I do all I can to keep the cats away from our yard