But what's the difference between the relationships except for the piece of paper? Especially given that Dick was the kid he actually raised for most of his life? I doubt Tim or Jason would ever consider himself a son to Bruce where Dick was not.
I don't think it's the piece of paper that matters at all, just the fact that at the time he took Dick in Bruce himself was very young and not really intending to be the parent in the sense that he was with Jason or later, Tim. At this point it certainly doesn't make him any less Bruce's son, but it does change the dynamic a bit for me, particularly whatwith the sliding timeline in current canon putting them at most maybe twelve - fifteen years apart. It's a complicated relationship, and even now there's really no one Bruce relies on more other than Alfred, maybe. Dick is a friend and a comrade as much as he is a son, simply because that's how Bruce trained him and initially framed the relationship, and I would argue that he always has been.