^I think that "who wins" is one of the least important aspects of the book.
As for Rorschach's character...first, your opinion seems colored by how much you value his "coolness". The man has serious issues which are expressed via an extreme worldview, and is a highly unreliable narrator. I think he's cool just as he is...he's a fascinating character who does really badass things. But seeing his flaws doesn't lessen any of that, it helps me to appreciate why he is the way he is. That's a very important element of this book--to postulate how, in a more realistic setting, anyone who would put on a costume and dedicate themselves to fighting crime would have to be of an extreme personality type.
I'd agree that he thinks about sex...he's clearly strongly repressing his urges. But, correct me if I'm wrong, there is zero evidence in the book of his ever having had sex or a relationship with anyone--male or female. There is also an utter lack of his expressing any positive regard for women, whereas there are plentiful examples of him berating whores and such...and of course, there's his often-expressed revulsion of women's clothing. I think that what his mother did turned him off of the opposite sex entirely, or at least made him completely suppress his urges for the opposite sex. The thought of sex morally disgusts him. That doesn't mean he doesn't biologically crave it. Hence the fact that he seems particularly violent against rapists.
Do adolescent males resent women? Or do preadolescent males...who are, essentially, asexual? You could say that Rorschach is a card-carrying member of the He-Man Woman-Haters Club...as many boys are, before they start to get those urges and women become objects of worship and desire.
And yes, I think that Veidt is either also asexual, or a repressed homosexual. We see zero evidence of romantic/sexual interest in anyone...except maybe himself. Perhaps he sees himself as so above ordinary people that they don't appeal to him. When he cites Doc Manhattan as seeing people as red and black ants, I think that he's really projecting his own secret views.