I went jogging in Brooklyn (Williamsburg) and stepped on a huge rat. Poor dude was just having breakfast in one of the garbage heaps on the sidewalk. Never experienced that in Europe before.
I used to live there and the rodent problem is real. There was a great book about it a few years back where they wrote up a little piece on each cat at each location. And yes, I had a cat in my house because without a cat you get mice.
Paris is also notorious for its rat problem. To say that Europe doesn't have rats is just silly.