Um, okay but neither of my Goldens would have bit any kid who ran at them in any manner. They wouldn't have bit the kids, it would have been fine. I think that is how the general public (including kids) thinks dogs act.
I am starting to realize that Jupiter has a completely different temperament. He is just naturally more bitey and less accepting of people and dogs than the Goldens were. He's been through puppy obedience, obedience 1, and now is in obedience 2, has been extensively socialized with adults, kids, and dogs, but he's still pretty unpredictable. Of course he is only 7 months or so and has been cooped up because of an injury, but he's obviously just wired different than the calm and accepting kind of dogs. Perhaps with training and maturation he'll become much more tractable, but we didn't do anything with the Goldens to make them that way.
When he was just a few months old, I used to take him to the park with my daughter. At first, he accepted kids petting him, but after a month or two, he would sometimes nip at them and I realized he couldn't be trusted around him. And of course the kids think he's a big stuffie and is cute, and they want to hug him or kiss him. Experience shows that they don't obey me when I tell them how I act. Therefore it's on me to keep him away from kids.
I always wondered how GSDs could be #2 in AKC registrations when I never see them walking around. Is this why I never see them, because they're hard to control?
Let's think about the breed of dogs you mentioned and how and for what they came to be. A Golden Retriever is a bird dog. Nothing wrong with that. They have the energy and ability to hunt with their owner. They were created for successful hunting, which means obedience in the field, and instinctive bird-dog behaviors, like hunting, pointing, setting, retrieving, flushing, etc. The Golden Retriever is the retrieving type. If they will flush a bird that's cool, I don't know. I do know that they are bred to be obedient even when doing what they were instinctively built to do. And they are bred to retrieve a bird without injuring it further, meaning they have a gentle soft mouth. At no point were they bred to protect the hunter from people or animals. That is just not in their job description. They are big like German Shepherds, but their down-ears and soft features generally do not instill fear in parents or children. That in an of itself probably prevents incidents. Will come back to that.
The German Shepherd Dog was created at a time when farmers in Germany were not loaded with money. They needed a dog that would both herd sheep/cows, etc, and not bother the chickens and other farm animals, but would also protect the family and farm creatures from both man and beast. It IS in their job description to be suspicious of strangers, especially if they are acting nervous. The upright ears, large teeth, and interesting reputation of the German Shepherd Dog gives a LOT of people pause. They are fascinated by the breed, but a little afraid of it too. They want to be brave and they want to pet the magnificent creature, but they are also wondering if it will bite them. If I had a nickel for every time a stranger offered my dog their hand to smell and then ripped it back when the dog started to sniff the hand, I could probably buy something real. The dog is bred to be obedient and work with their owner, and to sometimes work independent of their handlers.
I saw a early German tape/video from 1920s I think of a German Shepherd Police dog walking the beat. On its own. Finding a drunk man and alerting, not biting the dude, but his handler was able to come up on them and take over the situation. Interesting. The way the shepherd works sheep with a dog in the US is different in Germany. The dog in Germany has to move 200-300 sheep or more down a busy thoroughfare, keeping the sheep out of the road and out of the crops, to get to the grazing land. The numbers the dog is working makes it impossible for the dog to get a lot of support of a shepherd.
Because of their trainability and intelligence, both Golden Retrievers and German Shepherds have been used for Seeing Eye dogs. They are different here too. The GR will do exactly what the blind person wants, every time. The German Shepherd may be more likely to employ disobedience when necessary, or even find a better route/way to do something. This can be good and bad. Also, most of the blind-person with seeing eye dog muggings happen when the seeing eye dog is a bird dog -- lab or Golden, and not a GSD. They are different creatures and made for different work. You can still see a lot of GSDs used for police work. GRs may be used for sniffing bombs, but rarely are they full-fledged police dogs (here in town we have had a Labrador as a police dog -- not impossible) it just isn't their forte.
Now, when does a dog bite? A dog bites most often when they are afraid. When a dog is comfortable, and the people around it are comfortable, and no one is giving off any bad vibes, bites are not the norm. So, your GR is probably perfectly happy to have children run up to it, it is not in his job description to protect you or himself, the children are not nervous and probably the dog has enjoyed many of these scenes from puppy on up. The German Shepherd dog commands some respect, even from children. Children may run up to them, but probably a lot fewer over the year of upbringing than the friendlier-looking GR. Adults and children alike are a lot less nervous around the GR, so the GSD who has had fewer encounters of this sort, is now faced with tension often coming from the strangers, maybe from the children, and very possibly from its own owner, who has probably tightened the grip on the leash which immediately tells the dog, "it's going to get real."
A child or adult who is not nervous around the dog, is going to offer their hand in a relaxed fashion that the dog will sniff and receive pets for. The owner is happy, and everything is fine. The child or adult that is nervous, you might think, will be slow and careful. Maybe some are. But when someone is scared, they are much more likely to shoot out there hand, take a swipe at the dog, and then pull their hand back quickly. What NOT to do. But that is what they WILL do. What self-respecting GSD is NOT going to try to grab something shooting toward it, probably toward the top of his head??? What self-respecting GSD is NOT going to go after a retreating hand, especially when he smells the fear all over the person??? It is actually pretty amazing that not more German Shepherds have left scars on people.
Understanding the dynamics of the breed and the fear/reputation, what goes on, is helpful in setting your dog up to succeed.
Don't think puppies are safe. They are not. Rushie was not more than 4 months old when a full grown, big man was scared to death of him. Dark shepherds, Black shepherds are often viewed as more likely to bite from folks that are afraid. Not sure why this is. Rushie was blanket back, that looked bi-color, and the sweetest dog ever. But everyone wanted to pet Babsy and Jenna, either of them who may have bitten giving cause, whereas Rushie was very unlikely and got a lot less requests. I think because he was much blacker. I've been lucky through the years. I have had a five year old run up and throw his arms around Cujo who was out with me, but lived with my parents. He didn't do anything, but if he did, it would have been tragic because I was trying to pay for something and didn't see the kid coming. I was paying for his grooming. So he had to be there. The kid's owners should have been whipped for letting her do that. I left before I let my mouth get me in trouble.
We have chosen to own dogs that have protection, which includes biting humans, as a part of what they were bred for, so we have to be careful when we have them out. We cannot tarnish their reputation further than it is already. We need to be ultra-responsible with our dogs. We need to keep them safe.