There's really no comparison...
Rewards reinforce behaviors and make your dog perform those behaviors more frequently. Punishments inhibit behaviors to make your dog perform them less frequently.
Therefore, to train a dog, you simply reward desirable behaviors and punish undesirable behaviors, right?
Not so fast.
When you actually compare them, it becomes clear that Rewards are a vastly superior form of behavior modification, and that Punishments are so difficult to use effectively that they're often counterproductive and unnecessary.
Believe it or not, it's actually easier to inhibit undesirable behaviors using Rewards instead of Punishments!
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Rewarding your dog is easy. Every time you reward your dog for doing the right thing, you're taking a step in the right direction, you're reinforcing good behavior, and you're strengthening your bond with your dog.
Effectively punishing your dog is very challenging. It's easy to do something aversive or unpleasant to your dog and call it a "punishment" but a real punishment will inhibit behavior and all too often, the things that people call "punishments" don't inhibit undesirable behaviors. If they did, the need for punishments would decrease as the frequency of the undesirable behaviors decrease. Pretty soon, there would be no need to punish any more, because the undesirable behavior will have ceased. But it rarely works out that way.
The big problem is that punishment must be immediate, consistent, and comprehensive. There are so many ways that your dog can behave that you will not like. With punishment, you have to punish every single one. AND you have to punish them all consistently, otherwise your dog will learn when they can do what they want or need to do without anyone noticing. AND you have to do it right away, otherwise your dog won't understand the connection between the behavior and the punishment.
All too often, punishments just train dogs to do undesirable behaviors when no one is watching or paying attention. And it's not that your dog is being sneaky or devious. They're just being a dog, doing normal doggy things and if you punish them for doing these natural doggy behaviors without giving them an appropriate outlet, they're going to look for times and places when they can fulfill their doggy needs.
The one thing that every aversive punishment reliably and effectively teaches your dog is that you can be a real jerk sometimes, and that they should be wary of you.
It's important to note that rewards are almost always safe to use, and usually make dogs less dangerous, by helping them feel more at ease and comfortable. Punishments, on the other hand, especially aversive, scary, painful, or unpleasant ones can be harmful and even dangerous, as they give your dog a reason to be afraid and wary of people, and this sort of fear can lead to a dog biting a person.
With Rewards, inconsistency isn't just OK, it's helpful. You don't have to reward your dog every single time they do something good, in fact, it's more motivating if you don't. Just think about how much more motivating it is to use a slot machine instead of a vending machine. When you don't know whether you are going to get a reward, and you don't know how big that reward is going to be, it's very exciting, and that excitement will keep you trying over and over again.
There are a lot of ways that your dog can behave that are good, but you don't have to reward them all in order to make a positive change in their behavior. All you have to do is reward one good thing one time and you've already made some progress.
Of course, the most obvious difference between Rewards and Punishments is that one is Fun and one is Not. Rewarding your dog is fun, and makes your dog think that training is fun, and that you are fun. Punishing your dog is not fun, it makes your dog think training is not fun and it makes your dog think that you are not fun.
Of course, the reason people think punishments are useful is because dogs sometimes perform undesirable behaviors and people want a way to reduce the frequency of those behaviors. Fortunately, you can use rewards to achieve this goal. Use Reward Training to teach your dog to perform desirable behaviors on cue, reliably and promptly. Then, when your dog is doing something undesirable, tell them to do something desirable instead. And when they do what you ask...
REWARD them!
(If you're interested in learning more about how to train your dog to perform a behavior on cue, reliably and promptly, check out this Dunbar Academy Downloadable Document about how to teach a Super Sit)