"It could be that he gets along better with older kids because they're "picking up the slack" and more tolerant of his social weaknesses, since he's younger. Kids his own age might be less tolerant."
I completely agree. This is frequently the case. Also, lots of children are good with smaller kids because the smaller kids do what they want.
It is MUCH harder to negotiate with peers because they are on equal ground.
He also might be more bossy with children his own age because he knows he's more articulate. "I explained fully why you should be my sidekick and carry my stuff, and you didn't object clearly and to my satisfaction. So do it, because you haven't given me a good reason not to."
Their response: "Oh, p* off."
Commence argument. The verbal child continues because he doesn't understand that the argument is over. He doesn't recognize this because he was playing a different game (namely, the one he believes he can, and did, win: that in which he uses his verbal skills to argue a point).
If that is the case, then it will get worse with age, and he needs to know that people aren't obligated to use reason in social interactions. They don't have to be your friend, do what you want, care about what you care about, listen to you, etc. and that's totally fine. People do what you want when they get something from you, not because they have beliefs about what they ought to do or how awesome you are or they are convinced they "should" like something.
This is hard for kids with ASD or other social delays to get. And it doesn't have to be severe. There's a girl in my neighborhood who is not socially delayed at all, but who is used to being leader of the pack.
Once I told her point-blank: "You don't get it. They don't have to do what you say. Just because you want to do it doesn't mean anything. It just means YOU want it. They are their own people and they will do what they want, and what they like, just like you. And that's okay. And you have to leave them alone, because trying to make them do what you want is wrong, because it's irritating. You can invite but you can't force or badger them. PLEASE STOP."
Her mom had said the same thing in so many words, but she hadn't listened. After that it got a lot better, but the same kid (who has no problems at school--I get the feeling she's a bit of a queen bee there, not cruel-hearted but definitely bossy) still says, "But when you don't do what I want, I kind of feel bad."
We just keep repeating, "Yeah, life is hard like that, having to compromise. But you're getting better at it. Keep trying!"