We have this same problem ,last spring we started to let our American short hair outside , he does not stray to far and returns when called , he is not a declawed helpless cat but a young 2 year old male who loves to spend time in the nearby woods as any cat would , but last summer when our short hair would come home our 14 month old Savannah male would attack him as he entered the rear door , he is no match for the Savannah and stressed out going thru the door into our house because a attack was common even with water bottles ready, our Vet said it's a territorial thing ,Tigger has something Cody doesn't have and that's the problem, I realized our Savannah cats need some room outside and at the time as they watched out the kitchen window their outside run was being built, when it was done the pressure was off Tigger , Cody had to cat up and see the outside world, Cody does not attack Tigger like he used to but he will still play hard and we have escape points for Tigger through out the house.