Tommy'
In Ohio the 'cats are protected. But, I have seen films of bobcats slinking in to the caller, and stopping at a good distance before coming further. 'Cats, unlike coyotes, will take a much longer time to come in -- and they may bust your setup before you get a close-in shot with a .22 Hornet.
The .223 with 40 or 45 gr' pills will reach out there (250+ yds) and take a 'yote or 'cat whereas the Hornet can't get that kind of reach with that level of killing power. The .223 is also capable of target-grade accuracy with readily-available components. The Hornet brass is usually more expensive, with the cartridge itself (in my opinion, lest someone start crying!) being more finicky about load development.
I'd have a lot more faith in a .223 for putting down a varmint or a deer right where it stands as compared to a .22 Hornet.
SS'