I hear Americans talking about cockroaches a lot, but I don't think I've ever heard anyone from Scotland mention having them. I can only assume we don't have as big a problem with them. They seem to be rare.
Mice on the other hand...
Cockroaches thrive in hot climates, that's why they were such a problem in Phoenix and when I was stationed in 29 Palms, both in the desert.
Cockroaches are a lot more rare out here on the coast where it is a lot cooler. Ants on the other hand, are a huge problem.
When I was in elementary school, the ants always targeted the lunches we brought to school. On average, 1 kids lunch got eaten by ants every week. It happened to me 4 or 5 times.