No they aren't. Sounds like you dog picked up a bad habit which you were unable to break it of. Dogs don't normally become obsessed with killing tweety birds. They do have suppressed natural instincts to hunt rodents and larger game birds like pheasants and grouse. Usually you have to work with them to bring that out. They are quite content to depend on you to fill their dog dish and fetch the stick, which is why dogs are so loyal. It's all about the food dish for them.
Plus, there aren't packs of wild dogs roaming around in numbers anywhere near the numbers feral cats. You might be interested in using google to look up statistics on feral cats and the number of song birds they kill annually.
Dogs like to hunt. They like to hunt things that move. Everyone I know either complains about their dogs killing birds, or brags about it.