I don't believe that cats should be allowed to roam freely outdoors. As Rapaire pointed out, cats are carnivores - but that doesn't mean you are stifling their behavior by keeping them indoors. Cat toys, playing with your cat, and even moving their food can help stimulate their instincts and keep them from becoming bored.
Whether or not cats are diminishing bird population is not the big issue. Cats are under tremendous stress outdoors - fighting for territory from other cats as well as animals, danger to cars and humans, etc. They have more opportunity to be exposed to disease and injury and you will shorten their potential lifespan by keeping them outdoors.
Just as humans have learned to move out of caves and hunt their own food, cats have adapted to modern times. There is plenty of stimulation indoors. I highly recommend having at least two cats.