Cooper sounds a lot like Jackson. He's never gotten into a fight with another dog so I really do not know how he would react. At the dog park I'd say he's more laid back than aggressive. He may sniff another dog but will do it very quietly, almost secretly while the other dog is not looking.
Max has gone to the dog park twice. He's very shy and doesn't like to sniff or be sniffed. He did, however seem to get a little more interested in the other dogs the second time.
Max gets a little close to another dog and then runs like a mad man. I see his tail wagging so I do believe he's playing. However, when the dog that is chasing him finally reaches him, Max will go from a full speed run into a rollover, play dead fainting goat!!!
I think the other dog thinks he's dead and walks away. Max then gets up, wags his tail and walks away. I've seen him do this about 5 times now. It's very bizarre and I'm afraid he's going to hurt himself going into a dead stop. I don't imagine if a fight started that he would fight back, although when he and Coop fight he is a little more aggressive and has more of a temper. Cooper is moodier but only growls. He would never start a fight.