You know what the worst thing you can do to a show with a psychological theme? Make it star a slightly older Shinji from Neon Genesis Evangelion. I can't for the life of me understand the thought process behind making someone so useless as the male lead. To build a harem around him is even dumber, unless you are doing a parody of anime cliches. But no, Chaos;HEAd takes itself entirely too seriously for something as self-aware as that.
It's a shame, because there is so much working for Chaos;HEAd. There is a lead character that doesn't know if he's hallucinating or not. There are plot threads everywhere that mold together into coherency (eventually) that make the cast have relevance. The artwork is Madhouse, meaning that the aesthetic standpoint is powerfully executed. There is mystery, there are moments of tension, plenty of ominous moments, and some clever combination of metaphor in writing matching up with artistic license from the visual aspect.
Chaos;HEAd is a show that you can't decide if you like or not and then it ends. It is as thought provoking as the amount of thought you are willing to put into it. The psychological aspect isn't particularly deep, but it is definitely well executed. It could have been magnificent had the lead character had half a modicum of charisma. Not since Shinji have I ever felt like beating someone up so much. He is characterised perfectly from his absolute cowardice to the cringe-inducing whiny voice acting. The one saving grace as that he mans up at the end rather than remaining a whimpering wanker.
So, did I enjoy it? Well, just like the other ; work, at the start it was more interesting than enjoyable, but has an engrossing feel to it. It grew on me though. It isn't particularly deep, and the twists become obvious. And yet, Chaos;HEAd becomes a satisfying experience. Even though each arc has an ultimately cheesy and obvious ending, it doesn't change the fact that the resolution feels right and helps clear up most of the series (though there are a couple of glaring holes left in the plot that you might forget by the end). What can I say, it's rather fun in the end.
Writing (Story and Characters):
Chaos;HEAd is ultimately the prototype to the wildly popular Steins;Gate in writing style. It is far less refined, but also uses characters who aren't particularly likable at the start, bouncing between reality and possible fantasies. There is a lot of "tech tech the tech"s to explain the important plot points (the famous Star Trek writers' phrase for insert "psuedoscientific BS here"), but it doesn't really matter as long as you don't think about it too hard. While there are technical issues in the way of holes in the plot, inconsistent characterizations, and a helluvalot of other flaws (which Steins;Gate dealt with far better), in the end the writing is engrossing.
It may seem complex, but Chaos;HEAd's story isn't, not really. The ending is cheesy to the extreme, and you can see it coming from a mile away. There are holes in the plot and forcibly "ooh that's dark and edgy" moments. There are issues with everything from an inconsistent tone, whether the show decides if it is dark at a given moment or not, missed opportunities for greatness, and so on. Yet there is no doubt that the story is not standard, and it pays off.
As to the characters, what can I say that isn't insulting. The main character for most of the series is Shinji 2.0, and then becomes "standard shounen hero" in the end. Some of the other side characters have stock personalities. The interactions are forced, and the harem(ish) touches are so artificial that it's painful. The backstories are overly angsty to the point it is nearly laughable. The character development and resolution are cheesy to the extreme. But despite all these huge technical flaws, the cast is balanced and it gives a general warm and fuzzy feeling (and has moments of greatness, like the detective girl when she's aggressive - not tsundere, but intimidating as hell).
While you might think of what I wrote about the technical flaws of each quite a bit, I did like the writing of Chaos;HEAd quite a bit. It isn't genius. Steins;Gate which was basically the same staff in their next showing was executed far better using similar literary style and themes. But, extra credit for attempting to go outside the box, and as opposed to most anime going for something that feels different (except for the shounen ending). Technical issues aside, the writing is enjoyable.
Art (Animation and Sound):
Really, it is not easy to analyze how good the art of Chaos;HEAd actually is. There are moments where it is downright brilliant, when the audio and video make a hole in the plot completely irrelevant by stealing the show. There are others where you just can't miss the corners cut for budgetary concerns. In the end, it is a mixed bag. Overall though, the quality is high, and the artwork memorable.
Madhouse have done better than their work on Chaos;HEAd. Sure, the character designs are distinct. Yes, there is some beautiful use of style to make the relevant parts of a scene pop. There are moments where it may very well wow the viewer. Still, the palette choice for the series is a bit on the dull side, and while the backgrounds are diverse and detailed, they aren't really memorable. There are too many moments where you can see that a part of the scene lacks motion which is one of the more obvious ways to lower budgets, and it can get annoying at times. Still, it is a strong showing overall, as even on their off days the Madhouse crew does a good job.
There are less issues with the audio other than the glaring one: the main character has an annoying voice. He is supposed to have that kind of voice because he is an annoying character and it fits well, but it still annoys the hell out of me. There aren't any moments where the audio will wow you, but there aren't any moments where it doesn't fit. It is solid, and the soundtrack is surprisingly good. Still, I can't really say more than "it is somewhat above average" due to my one subjective issue with the annoying voice of the main character. I don't care that it is right, when what is right annoys me.
Chaos;HEAd has solid artwork. This is a great contrast to the writing, which is everything but. It is a balancing act of trying to tie down the plot into a more grounded world, and it is effective in doing so. There are few technical issues, but they are there. As much as I dislike the main character's voice, it is the correct choice for the series and how it plays out... so while I dislike it, I cannot rate it lowly from an (attempted) objective standpoint. Ugh, it is not easy to judge. Above average, obviously. Good, and at times great. But not magnificent.
Overall:
Chaos;HEAd is more interesting than enjoyable. And that's fine. You can see how it is the first attempt of the crew behind Steins;Gate, but is far less refined and powerful a work. But what can be said is that the show is quite good overall, if you can ignore the slew of technical issues that plague everything.