Loki and Terra always have two barriers between them when humans are absent. Loki has run of the house these days, while Terra is in a crate shut in a bedroom. I feel comfortable narrowing it down to one barrier when I am supervising. Example: Loki loose in the yard while Terra is in her privacy fence pen, or Terra loose in the house while Loki is shut in a bedroom.
Both are females of differing intact status. One raised with the other from puppyhood. Played well for the first year. We had a male the same age as Terra, and he ran with the girls. Eventually, we ended up with a scrap between each pair. Spent a rough period of time figuring out who could go with who under which circumstances. Eventually worked out the system, but not without scarring. Which is why some APBT folks just keep their dogs separate full-time. I prefer to allow them to socialize under control until it can no longer be that way. Hope for the best, prepare for the worst.
Loki's main issue is a lot of need for personal space and respect-mah-authoritah! SHE will initiate play when SHE feels like playing. Otherwise, her alone. She's laying in the sun? Don't sniff her. She's got anything in her mouth? Don't look at her. Someone in the room eating food? Don't breathe in her vicinity. When she's feeling sociable, she's great with other dogs. She's never scrapped with a non-APBT. Her first fight was when another dog ran up on her outside the ring at a show and grabbed her; she reacted by crying and then fighting back. Since that time, she has gotten progressively more offensive and willing to go the second she feels the tension. She will offer normal warning behaviors sometimes, but if the other dog wants it for real, it's just on. That fast.
Terra's issue is more excitement/redirection, as well as probably some predatory drift. When we had Priest, he used to vocalize a lot, and his barking would spark Terra glomping on his head. She could escalate in play to fighting, which makes her tricky to deal with. These days she could play with a male dog as long as he is not excitable or overly vocal. I wouldn't even try her with another female. She has barrier issues as well. I used to crate her and Loki in the same room and let them loose in turns. I was coming back to Loki's crate bloodied from the outside when Terra was loose. Last big fight we had was when Terra got excited and hit a canvas crate Loki was in. Loki hit back from the inside and that crate just disintegrated.
Now when we had Priest -- intact male -- he was very good with his girls even when they were not good with him. He would fight back when attacked, and sometimes unwittingly provoked the fight in the first place just by being a dumbass. But the only time I ever saw him start a fight was with a complete stranger (a spayed female). So I would say Priest was the typical territorial male. He had his girls, no desire to make friends with any other.
So. I've had the experience of different types of aggression in this breed, all with the same bloody results. Male/female pairings work the best, but even that is not foolproof. I am going to say that in my experience the power is an issue, but the big difference seems to be complete commitment to the task at hand. 0.5 seconds in, those dogs already know they're going to kill each other. No tapping out.
Sometimes if it starts as a misunderstanding, they might cool down and be able to hang together again after its stopped. Or sometimes they really seem to take it personally after that. I think Loki and Terra's first throw-down -- in which they never got holds and in which Priest danced around the outside and nipped them, "fight, fight!" -- was an unexpected thing for them. But when reintroduced later, they were both tense and it just started up again. So they have been separated since then. Things have settled a bit where I can at least travel with both dogs crated and no drama, and we can take walks with two handlers. They don't spit fire and threaten each other. And sometimes they will sniff at each other like normal dogs interacting. But if they are close enough to reach, they will go.
There are obviously dogs that never have a problem, and I have mixed feelings about said dogs. I'm happy they can live life as normal dogs. But they impress the minds of newbies and said newbs think we must be exaggerating when we talk about dog-aggression. Or they wonder what is wrong with our dogs that they cannot be together.
My vote is to allow for sensible socialization, but for the love of all that is good in this world, be prepared. Set your dogs up for success, and don't get caught with your pants down.