If supernatural mysteries are your thing, here are two series with a lot in common on that line. Great characters and great stories bring both pseudo detectives stories to life with an array of the supernatural that makes them both work. :)
Not sure who copied who, but the settings for the mysteries in the first few story arcs of Kindaichi Shounen and the story arcs of Ayatsuri Sakon are exactly the same. The castle and being stranded in an isolated mountain - all too familiar. But both are good regardless. And the mysteries are different even though the settings are strikingly familiar.
Compared to Ayatsuri Sakon, Kindaichi is your stereotypical shonen hero: He takes action, loud, funny, good hearted but deep down he has a sharp wit. At first, this might seem like a huge contrast to Sakon, considering how shy and soft spoken he is but the overall plots of these two series are pretty similar. At first the cases present themselves as supernatural, but soon the protagonist unravels the truth. If you enjoy mystery animes and are looking for something similar to Sakon but a little more lighthearted, Kindaichi is a great follow up series.
For anyone who enjoys a collection of good mysteries, I recommend Ayatsuri Sakon. Being classified in the same genre as Detective Conan, both series share a common ground. Whereas I view Detective Conan as something fun that could be watched for entertainment, I found Ayatsuri Sakon to be more believable and enjoyable when comparing the two. One of the best things I liked about the series is that all the cases are never solved within an episode, whereas the majority of Detective Conan cases are often solved within that time frame. I find this helps to keep your interests in check throughout the series, as well as giving you time to form your own conclusions. For anyone who enjoys mystery, I strongly recommend Ayatsuri Sakon.  read more
Both Anime's have a rather dark side to them, yet still manage to have the lightness that is needed to pull it through to be very likable. I also see Sakon carring Ukon around all the time, and Razel ends up carring around her teddy bear.
Both involve mystery, one slice of life/arc based, the other built over a scattered timeline. Both deal with supernatural. (Sort of, depening on how you look at it). Both happen to also take place in a yester year, have a similar Gothic style, not to mention interesting characters.
Both are from the mystery genera, with a possible supernatural twist to them. I say possible, because whether or not Ayatsuri Sakon has that, is interly up the the veiwer, whether Ukon is a possesed puppet or not.
They are both mystery series, though Ayatsuri Sakon plays in it more. What drove me to recomend it more was the concept of 'puppets' that run through both shows. Also, the opening to Suteki Tantei Labryinth has some things that remind me of the closing for Ayatsuri Sakon.
Both have puppets in his main story. The protagonists (Tachibana -Sakon-; Rangiku -Karakuri no Kimi-) are puppets masters and both saved a past history.
While the theme is different, Karakuri Zoushi Ayatsuri Sakon have detective histories (and a better argument) , while Puppet Princess has shounen and martial parties, both are horror genre.
One point of similarity is the background music. Both are very good (better in Miyu) and it express the suspense that needs the work.
Also both are horror stories where there are always crimes.
Miyu is more than vampires and superpowers while Karakuri is more detective
While both of these anime's are of different genera, both have a very simular goth vibe to them. This is rather hard to explain unless you watch it. The coloring is simular and so is the depth on the characters.
Ukon and Kenchin look very much alike. This is due to the fact that the two manga artists supposidly worked together early on. This being said, while they are different genera, the styles of the artists are very simular.
The shows both have a rather gothic look and are mystery based. The character designs have simularities, having a detailed look, yet not going overboard with the details. The characters also have depth in the characterization. The two main characters, of the two main male characters, one is serious, one is more comedic.
Another "supernatural" series with an interesting lead character. Supernatural is in quotation marks because Ayatsuri Sakon usually presents mysteries with supernatural clues but always ends up being a person's evil scheme. Much like Ginko, Sakon acts like a detective to unfold very interesting mysteries.
Both animes contain a series of detective mysteries the characters have to solve. In Himitsu it is done through looking into a dead person's brain, in Ayatsuri Sakon the mysteries are solved by a young puppet-master using his doll for it. Both animes explore the dark corners of human souls.
I don't wish to give away much of the plotline of the movie, but let's just say that mechanics and injunuity, much like the mechanics for puppets like Ukon, are invovled. Plus, Kito Kid and Sakon are both ventriliquists...