There are a few studies out on the effect of cats on birds. Nearly all of them show a negative effect of cats on bird populations. I only came across a single paper by Courchamo and colleagues in 1999 that show a positive influence of cats and this is a modeling paper.
One of the more interesting studies was Crooks and Soule's investigation of the interaction between cats, birds, and coyotes. Where there are more cats, there are fewer birds. Where you have coyotes, there are fewer cats. By analyzing scat, they found that coyotes were eating cats and the assumption was that there were fewer cats eating birds. But were the cats actually eating birds?
A new study (link to press release) by the University and Georgia and National Geographic's Remote Imagine Department actually show cats catching birds and other animals. When I say show, I don't mean demonstrate through experiment, I mean there's video!
How many birds? Their estimate is 500,000,000 birds per year. I'm not sure how they included feral cats, which must kill "professionally" to stay alive.
Will be interesting to see where this gets published and the public reaction.
COURCHAMO, F., M. LANGLAIS and G. SUGIHARA. 1999. Cats protecting birds: modelling the mesopredator release effect. Journal of Animal Ecology 68: 282-292.
CROOKS, K. R. and M. E. SOULE. 1999. Mesopredator release and avifaunal extinctions in a fragmented system. Nature 400: 563-566.