As a Pilgrim breeder, I suspect that there is a fair amount of confusion in distinguishing the breeds, which may lead to possible crossing of Pilgrim and CP stock because of their similar physical traits. With the obvious exception of the saddleback coloration found only in CP, the two breeds (to the untrained eye) can look nearly identical.
According to the Livestock Conservancy, the two breeds should be similar in size/weight, with CP weighing in at around 14lb(M)/12lb(F) and Pilgrim at 14/13. LC's
goose breed chart shows that the Pilgrim is a significantly better layer than the CP, if that's important to you.
I've been working with this breed for several years now and have - to my chagrin - been sold hatching eggs and birds that turned out to be either poor examples of the breed, suspected mixes, or another breed (Toulouse also have somewhat similar coloring), early on in my foray into raising the breed. If you're looking locally, I caution you to be very careful about ensuring that you're getting true Pilgrim stock, and to buy only from reputable sources.
That said, I find Pilgrims to be fascinating birds and an asset to a small farm. None of my birds, even during breeding season, is aggressive, though they can be quite protective of nests and goslings (which I think is a positive attribute).