Labs and Goldens are often top dogs in obedience at the national level. I think all the winners last year were Goldens. Shelties are pretty popular in obedience, Border Collies, too. Locally, we have a lot of Aussies, Border Collies and Belgian Tervurens that do well. There are a handful of Goldens and, if Janice Gunn comes down to show, we might have more than a handful of Labs. Oh, Papillons are kinda popular around here for obedience and do well. Don't forget the Poodles!
For Rally it's really a crapshoot. Even at your local Rally shows, you see a huge variety, probably more so than obedience. I just looked up last years AKC national winners and the number one dog was a Golden followed by a Belgian Tervuren, a Boxer and a German Shepherd. Locally for the past two trials a Papillon and a Frenchie went high combined in Rally. Rally is interesting because a perfect score is much more attainable than in obedience, but you are also timed.