Interesting to read the Red as a pest. Assuming we are talking about the same Red.
It (the species I am familiar with) is smaller than the Grey by some margin.
Here are the varieties I am talking about (photo courtesy of Morelle, 2008)
Indeed in the UK, the native Red has all but been wiped out by the NA Grey that came over with the merchant ships. There are a few enclaves of Red still in Great Britain, but very few and only because of active conservation efforts, providing "Red-sized" feeders etc....
Elsewhere the Greys have killed off or out-competed Reds for food and territory.
Definitely a case of Grey Devil on this side of the Pond.