I had two cats from the same litter. The female was superfocused on birds, rarely paid any attention to mice or voles which are pretty abundant here in the countryside. She very rarely managed to catch any birds in the wild, but if one made the mistake of flying into the house, it was game over in seconds. She could jump surprisingly high.
The male on the other hand was only interested in rodents. It was like to him birds didn’t exist. For yeard he kept our house totally free from mice, roaming the yard and doing his thing very effectively. I’d pay good money to have a cat like him again.
I wouldn’t let my cats out in the city, but out here I’ll let them live by their insticts. The nearby highway kills a lot more birds and mammals daily than they ever could.