The fact is The Joker didn't care about winning. He was in a win-win situation. Get Batman to quit and he runs riot. Batman doesn't quit and he still runs riot but gets to taunt Batman in the process. Harvey Dent and the Gotham City public were just pawns in his game, he couldn't care less how corruptible they are because they can ultimately be terrorised - the more opposition there is the more fun he has.
So, in truth, Batman won because he and the people of Gotham city (those that he is there to protect) remained incorruptible (despite their efforts to kill Reese), and survived to live another day. The only way the Joker could have won was if Gotham had descended into anarchy and Batman had given in, leaving him to rule the roost.
Harvey Dent was Batman's hope to lead the people of Gotham in defiance of the criminal fraternity, but the fact that he was eventually coerced into evil only goes to prove what a hero and a blessing Batman is to Gotham. Batman has lost just as much as Harvey Dent, if not more, but he never discarded his principles and thus remains Gotham's defender.
Simply put, as long as Batman exists his enemies will never win regardless, because Batman and everything he represents/inspires undermines all that his enemies aspire to. That's why, eventually, all his enemies give up on trying to create anarchy and go after him, then find they can't defeat him and try to create anarchy, then fail and try to destroy Batman, and so on, and so on.......
Batman wins!!!!!!! (unless you include actually having anything resembling a life, having a family, not watching your friends and innocent people die constantly etc.)