The advantage of purebreds? You get a dog with a set of characteristics that, within a range, are known. If you get a border collie, you know what the drives, coat type, etc. will be. You know you won’t get a border collie that has a wiry coat. If you get a Airedale terrier, you know you will get an intelligent dog with specific grooming and training requirements.
If you get a mixed breed, you get a guessing game.
The advantage of mixed breeds? Since the only reputable place to get one is a shelter or rescue, then you know you have saved a life, and haven’t paid a lot for the dog.
Mix breed dogs are thought to generally have a higher immune system than their purebred counter-parts but ALL dogs can get “genetic disorders”. Any dog is only as good as its parents. If the parents, even if they are also mutts, have genetic conditions such as vWD, Hip Dysplasia, luxating patellas, etc., then their puppies have a chance of getting them as well.
Also interesting to note, purebred dogs are far less common in shelters (they are estimated to make up about 25% of dogs in shelters)