Among other things, it's because he's probably alot more human than most other comic heroes. Punisher's human, of course, but he strikes me as a real vigilante, a merc with several chips on his shoulder no different than any soldier with a slew of weapons. Batman is a rich boy who doesn't waste our fucking time being a stupid rich boy. As Bruce Wayne, he's a billionaire with altruism in his blood, which we'd prefer more rich people were in real life. As Batman, he is many things.
He's a different style of crimefighter in that he's also classic for having been around a long time. You cross the masked mystery man who uses the shadows to his advantage with someone who has also studied hard in detective work and backs it up with resources to make it all work, so that people believe that he is maybe not even human, that he's all-seeing and terrifying to behold. Half of the dark knight's work is through criminals being too AFRAID to commit crimes, all by putting on a rubber suit and swinging around a bit. You can't get that intimidation with a gun-toter.
This is not to say that the Punisher is bad. He's clever, he's got the equipment, and he's frigging deadly. But to any person he meets, he seems human. Batman made his reputation making people think he was MORE than human. And then when they finally figured out that he was just a man, he caught them off guard by being a hella-smart man, a well-disciplined and trained man, a man who uses the unexpected quite alot... In short, Bruce was always ahead of the game. Maybe it's because he had money or that he had tragedy long before Punisher to set him on the path, but he got there first and he held the lead.
