Presuming you mean wild birds and not some of those vast flocks of escaped macaws I've seen...
The big difference is that the birds are supposed to be there.
The cats should be in an animal shelter or someone's house. If not, they are a nuisance species and should be eliminated like coyotes, etc.
Now this is interesting.
I feed about a 100lbs of maize a week behind the house. I’ve got hundreds of Mourning, Whitewing, Urasian and the smaller ground dove, feeding there every day. Add in the fact that I’ve got 12 outside cats and you’d think it would be a dove massacre. That’s not the case, the cats are constantly hanging around the barn and feed shed or out in the pasture hunting the rats and mice.