Well, to compare, we'd first need to establish whether, on average, dogs trained using only positive methods were better-behaved than dogs trained using both positive methods and corrections. You'd also have to take into account which took longer, and which dogs were better-adjusted to general situations. Also, some dogs are simply better at interpreting what we want, or more sensitive to the withdrawal of reinforcers.
Also, we have to establish that people use pure +R methods because they work better, and not because they have an ideological opposition to anything they consider to be punishment, which is what I think the real difference comes from in quite a lot of cases. Those who acknowledge that correction has a place in training will use multiple methods because they know that some things are better suited to correcting certain dogs and certain behaviors by them than others. Whereas anti-punishment ideologues, by their nature, have only +R to work with.
It should be noted that, in terms of the amount of extinction of a behavior that it can produce, a 60-second time out, for a normal, social dog, is roughly equivalent to a brief shock. (1-2mA @ 30ms.) It can be inferred that it causes roughly the same amount of distress to the dog. Is a time out then as 'bad' as shocking your dog?
Similarly, are bitches abusing their pups when they mouth or pin 'em or even nip back for nipping on 'em too hard? I wouldn't think so, because the pup understands the correction at an instinctual or near-instinctual level, and the corrections are always applied in a consistent, fair manner contingent on the actions of the pup.
Is booby-trapping objects you don't want your pups to investigate with a can with some pennies in it abusive? (The goal is to have it fall and startle the pup, not fall -on- the pup.
) I wouldn't say so, but a single encounter like that can keep the animal off and wary of something like a firepit grill or a laundry chute for life, and most physical corrections that you could administer without causing actual damage probably don't provide such a long-lasting aversive impression. (At least not of the object you're trying to provide the motivation to not bother. Of you, on the other hand...dogs understand 'correction' but they don't understand abuse.)
Anyway. For a long time, dog training methods were mired in abuse -- similar to horse training methods. You broke a hunting dog or a horse, you didn't train it. Even now, so many people utterly suck at applying punishment to a dog, tending towards abuse instead, so people who actually care about animals have swung in the opposite direction, to the opposite extreme. I'm apalled now at the way that we treated the first dog my family had, and even now most people wouldn't see any problem with the way that we raised it. So there's even a good motivation to tell inexperienced owners to swing to the other extreme: because it's a lot harder to really screw up a dog with poor +R technique than it is with poor correction technique. But I've put a lot of study into behavioral science and dogs since then, and I now use very +R methods. However, I'm also aware of the power of properly applied punishments, and believe that they are, in general, good for the dog if properly, consistently, and fairly applied.