Well both of them are more than just will power. For example we constantly get storylines about how Batman doesn't trust anyone and is preparing plans on how to take down Justice League if it went bad. I can't see Hal being ok with any of that.
Bruce hardly ever trusts anyone who can have the world at their mercy. His paranoid nature just won't allow it no matter how many times that person prove themselves, as if anyone needs Batman's approval anyway. So when it comes to someone like Hal who had already turned into what Bruce always fears his fellow heroes may turn into, there's no way they can get along that well. He told Superman once that the only time he's inspired someone is when he was dead and we think he'll treat Hal well? lol They can be on the same page but I don't see them being close friends or anything like that. Not that they'd ever share a substantial panel time anytime soon to emphasize on their relationship anyway, if you can even call it that at this point. I doubt Bruce or any of the core JL members care much about Hal even being a founding JL member anymore since he never spends any time with them. He needs to be there first before we ever bring up the "trust" topic.
I never liked Bruce being written like a paranoid lunatic, you would think that since he is so well prepared that he would be able to predict if a hero goes villain.
But I do agree Johnny, we need more Hal on Earth spending time with his JL friends.
I think it really only happened after Parallax and any tension shown in the past has been a retcon. I don't recall them having tension before that. And then Batman's friction with Guy kinda bled into Batman having an issue with all GLs to a degree.
However, I can see where there would be tension at first. Hal is a man with a powerful weapon, which I can see being a trigger for Bruce. And Hal's apparently flippant or cocky attitude flies against Bruce's adherence to strict discipline. So combine the two and I can see why it might have been difficult for Bruce to trust Hal at first..... but only at first. After being on the JLA together awhile should have taken care of that, but y'know, writers like friction sometimes...