I absolutely agree with Amazondoc that purebred rescues do just fine in performance events, but with a modifier. When selecting a rescue knowing you are going to compete with that dog, you had better know what to look for. You better know a lot about proper structure if you are going to do something like agility, and you better know how to recognize if the dog is going to be biddable and if it has drive. If you pay a lot for a dog from known performance lines, the breeder has done the work for you and has bred dogs that consistently show these desirable traits. Doesn't mean you can't get a good rescue dog if you are patient and know what to look for. I compete with my rescues and we have earned titles in multiple venues.
Our highest ranked agility rough collie - he is a MACH 6 or something insane like that - was a rescue. His owner jokes that no breeder would claim him as one of theirs. True, he has a fairly ugly head for a collie, but just excellent body structure. He competed at the Invitational a couple years ago at the age of 11 still jumping his normal 24" height. He would have placed, too (ahead of all the border collies), it he hadn't knocked the very last bar on his very last run. There were a bunch of dogs like him at the Invitational - some breeds actually compete better if they don't adhere too closely to their breed standard. The top agility GSD was very small and lightly built, the top pug had a way more leg than pugs are supposed to have, the top Aussie was a mini (my Aussie owning friends really hate that LOL) - I could go on and on. I have seen the same thing in the obedience ring and in tracking, maybe a little less in the herding venue though. Herding instinct does have to be carefully bred, though I know a few rescues that have high level herding titles.
Anyway... there is no right answer to the original question. I have competed with inexpensive dogs that were other people's trash and have done well and the dogs were a joy to have in my life. But my next dog is going to be a very expensive collie. I am supporting this breeder because they are part of a movement that is dear to my heart: reclaiming the collie's heritage as the farmer's most versatile dog, not just a pretty show face. People who are part of this movement (including this breeder) have collies that not only win in the breed ring, but in addition work stock of all sorts, do tracking and SAR, do obedience and agility and flyball, and do carting and joring. The goal is to have collies with titles at BOTH ends of their name and are game to do just about anything.