I doubt that you'll get meaningful differences anyway. Briefly looking at String::Diff, I guess that it'll likely take at least quadruple the memory size of its input, because it returns strings with the differences marked. You can maybe try to port String::Diff to work with files instead of strings.

Also, I'm not sure whether String::Diff has a concept of lines, and also your registry dumps likely don't have a concept of lines. Maybe using an existing, external diff tool is an approach. Alternatively, look at Algorithm::Diff, but I don't know whether it has more benign memory requirements.