I don't really get the antihero thing. Batman's not an antihero. Even Miller's Batman isn't an antihero. Some kind of operatic god-thing, maybe, but what antiheroing? Superman's a bigger dick than Batman, hence "superdickery."
Batman, on the other hand, has been consistently passionate, compassionate, swooping through the night and taking out bad people, saving lives, and inspiring people in his stories, which is something we don't as often see with Superman or Spider-Man, and I think, psychologically, does boost him up.
Batman sleeps all day, goes to fabulous parties, saves lives all night, has endless money, has the best toys, has a family of friends and allies he's inspired and relied on, is respected at the highest and lowest levels of his world, and he's brilliant, handsome, charitable, and dates the most fantastic women on a consistent basis.