In the battle of cats vs. Rats, the rats are winning. New research finds that contrary to popular opinion, cats are not good predators of rats. The study -- the first to document interactions between feral cats and a wild rat colony -- shows that rats actively avoid cats, and only recorded two rat kills in 79 days. The findings add to growing evidence that any benefit of using cats to control city rats is outweighed by the threat they pose to birds and other urban wildlife. Source 9p.
Well I think this will depend on many factors. First of all the population of cats today (In cities) are far more domesticated than they were in the past. When you think of the old term "Alley Cat" it hints at a time period when people on average treated animals like they were irrelevant and if the cat wasn't your pet specifically you weren't going to go out of your way to feed it. These animal rights organizations didn't exist back then, so the majority of the cats you saw running around your neighborhood were not only homeless strays, but also fairly wild as well. In such a situation ofcourse such cats will attack or feed on whatever they run into that is their size.
This is in contrast to todays time period where many people would be willing to feed strays to the extent that even the cats themselves are hip to it and know that they will find better luck with food just meowing to a human near by than to risk life and limb against rats that are almost the cats size.