In the city you have no choice but to rely on your local animal control office for feral cat issues or for that matter any feral/stray animals problems. More often than not they'll live trap the animal(s) and remove them to a shelter.
From there the shelter will either destroy the animal (if its found to be mangy or unsociable) or send the animal out to other shelters that will try and place them in homes. Personally I'm a huge proponent of destroying any and all collarless strays/ferals. People will say that some of those are pets even though they're not collared and tagged. Personally if someone really loved their animal they'd have the proper collar and tags on the animal - and not let it roam at large. In regard to the idea of placing them - the way I see it is they get placed in homes and then get free again to terrorize a new area... and then animal control is called and it all starts over again. Just a waste of time and money. I'd always been a supporter of heavy punishments for people who let their animals roam at will. Personally I'd be happy with a huge fine for people whose dogs/cats are caught roaming at large. Make'em pay before they get the animal back - and if they delay in paying make'em pay boarding fees. If they refuse to take the animal back take'em to court. It'll teach people to be more responsible with their pets in the city.
Out here in the country animals without collars die. Dogs with collars are captured (or killed if they prove to be of a dangerous temperament) then the owners are called. If I see the dog again law enforcement is involved - WI has a statewide statute against pets roaming at large off your private property. Third time I see the dog on my property it dies.
I just hate it when people either can't or won't (most cases its the latter) give their animals proper training and keep control of them. My dogs heel till released from heel (usually to go do something else), sit till I release them (again usually to go do something else) and don't leave my property (I don't have fences). In fact they don't wander away from what I consider my yard since that's what they've been taught as being their boundaries. Now maybe I've got a leg up on most people since I do train dogs on the side but then it really doesn't take that much time and effort to properly train a dog and keep it trained. I don't know about cats except that when they roam at large they are very detrimental to the native wildlife so they are shot on sight.
This is who we are, what we do.