I voted that they are both just as damaged. However, I think that they're damaged in different ways and it manifests itself differently.
In a very real way, they're both very juvenile and adolescent. For Danny, I think that stems from his low self esteem and what happened with his brother Louie. He expects the worst from people and thinks he should be treated like garbage. He definitely has abandonment issues that stem from the incident with Louie, possibly more abuse/neglect in his childhood that we don't yet know about.
He shuts people out and is self destructive. He makes the worst choices imaginable. He has a problem with authority/father figures, probably stemming from his own father and the incident with Louie. Like Top pointed out so eloquently in her post above, all of the times when he deliberately defied Mac in Season 1. Also, there's the incident with Ollie, Rikki and the stolen gun. He trusted Flack, but definitely was shutting him out. Flack had to barrel his way in, and actually get VERY stern with him. All he got was a "You should have minded your own business" for his pains.
Then, the way he is with women, as Top also pointed out beautifully. He likes to be pursued, and then when he relents, he latches on and doesn't let go, unless he's treated well. Note that when Lindsay was being nice to him, he was cold and distant. When she got bitchy with him, he tried again.
Could this hint at more abuse? I think so, and I'd like to see that explored more.
Overall, the way he acts, it's like a teenager. He's at the same time very much defiant and shutting out, but not wanting to be abandoned. He's also very provocative and petulant. When he has an issue about something, he can get nasty, like with the cab driver's son in "The Dove Commission." Although, he did have the decency to apologize, and the self awareness to tell Aiden that he had "Issues with Gypsy cab drivers."
Lindsay, on the other hand, presents as being very needy, demanding and selfish. I think that this stems from the deaths of her friends when she was a teenager. It's like in a way, she's never moved on from what happened. She's put up a great front, but....in reality is very fragile and has a hard time dealing. I don't think she quite knows how to handle things, so when things get rough, she melts down or turns it back on the person.
Note that she wants everything on HER terms. I think that stems from being catered to quite a bit after the murders. She comes across like a needy, demanding teenage girl to me, like she's stuck in that stage of development.
Note that in "Manhattan Manhunt" we see the first chink in her armor, where she gets upset that Mac sends her back to the lab. Then, in "All Access" she has a meltdown over Stella's situation.
Season 3, all of it was an Emo-fest. She agreed to the date with Danny, then stands him up. When he tries to talk about it, she shuts him down. There was her meltdown in "Silent Night," too. Then, how adamant she was about going undercover in "Love Run Cold." That was just a bit odd to me. Then, the whole, "I don't deal well with Mothers" thing.....It reminded me of a teenage girl who's struggling with things, who'll wig out for no apparent reason. All of it.
Then, there was the part in "The Lying Game." To leave someone with just a card, not talking to them in person, or even leaving a phone message, that's just rather juvenile, IMO. Another thing a teenage girl would do.
Season 4, started out fine, but then when Danny starts shutting her out, and not coming to her on HER terms, she flips out, culminating in her Monologue of Doom. Then, there was the scene where Mac asks her to catch Danny up on what's going on, and she just slams the case file or clipboard or whatever it was into his hands and storms off. There was also the "this is hard" scene, the phone call in "Personal Foul," and the several times that Danny tried to talk to her about it and she shot him down. It all strikes me as being very juvenile, not something a woman in her late 20's/early 30's would do.
The same thing with Danny and Lindsay's relationship. The way I've always seen their relationship is as follows:
It's like a three day teenage love affair, culminating with a gropefest in the back seat. They have their fun back there, but the day after, they go to school with marks all over each other's necks and whatnot, and have horrid things to say to their friends, and it's nasty awkward for a day or two, with emo tearz and stony silences in math class, but then it's over, and no one knows what the fuss was all about.
They never talked to each other about what was going on between them. Any time Danny tried to discuss it, he got shot down, or told how hard he was to love. They never even talked after the events of "Snow Day." When Lindsay sprang her Monologue on him, using the word "Girlfriend" and saying she'd fallen in love with him, he looked so genuinely confused, Like he had no idea whatsoever.
Is Danny innocent. Hell NO. I won't say he cheated, or that he was poor Mr. Patient, because yeah, he chose to go there with Lindsay in "Snow Day", for whatever reason. He did shut Lindsay out after Ruben was killed. Even though she never tried to reach out to him, she did cover for him, (No matter that she looked put out doing it) and she did alert Flack to what was going on, which did put all three of their jobs on the line.
Contrast that with Danny's night with Rikki, and subsequent interactions. They were discussing it at every single turn. They talked about how unhealthy it was in the longrun to sleep together for comfort. It seems as though they were taking care to not hurt each other any more than they were already hurt by Ruben's death. They were open and honest with each other from the get go. Also, note that at no point, did Danny say that he was involved with someone, Not even when Rikki said she was leaving. Also, take note that when Rikki told Danny she was moving, they both looked devastated.
That's why I like Lindsay as Danny's friend better than his lover/girlfriend or whatever. I think on a basic level they're very much the same, and it makes for a very dysfunctional, codependent relationship.
BTW, all of the above is merely my opinion, and I hold no unwaverable convictions as to whether I'm right or not. I welcome the debate it will bring. If you have a contrary viewpoint, I'd love to hear it.