I think that really depends on the animals in questions. You can make generalizations, but it comes down to the individual animal's temperament. At our home for example, we have cats and dogs that have no issue with each other. Our cats even hang out with our rabbits and, when we had them, our birds. There have never been any scuffles, but that doesn't mean it could work for you. Our dogs have no issue with our free roaming goat (we live in the country :P), whereas some dogs have such high prey drive that they couldn't be trusted around her.
I believe it really comes down to your pet's personality. There are plenty of odd "animal couples" out there that work well :)