It’s really strange and unfair that you hear so little about this manga. Sure, it’s not particularly high-brow, but it’s madly entertaining, even addictive, has sympathetic cast, and the main mystery is intriguing.

The story is told in separate police cases (maybe I could call it procedural) and the storytelling stays at the level of, say, a fine TV-series. As I’ve mentioned, there are some silly moments, when mangaka tries to show off the characters, makes them cry or overdoes the evil face trope, but the core of the story is… healthy? solid? I like that in the end when it comes to the killing, they kill without much ado. Killing earns this series a 7. The main characters are slaves to their goal to the end, properly, and it helps to ignore the occasional “handsome yakuza in a good suit poses” moments. Oh, and also from the description it’s easy to think that this series is woman-targeted, but it isn't, at least not in the usual way. (Btw, I suspect that the cheesiness is due to the legacy of Sanctuary, but I don’t know for sure.)
The main twist here is that the story is focused on battling corruption in the higher echelons of the police itself. The protagonists try to look for the mysterious figure who wronged them, but they clean off smaller fries in the process. The author puts a lot of effort in explaining the complex structure of Japanese police and makes a good use of it in building the intrigue.
The worst thing about the plot I can say is that it becomes a bit too dense and slow-moving, since the author makes a lot of detours to extend the chapter count. It's not a series, where you can drop in and drop out easily.

What holds your attention even through the weakest moments is, of course, the dynamic duo of the protagonists. They are very different and complement each other well, their ties run deep, and both have complex personalities.
The story focuses more on Ikuo the detective, the younger and the more innocent one of the two. Among his police peers Ikuo plays the amiable klutz part, yet he is not liked - it's said he is too introverted. Ikuo offers most of the comedic relief, but the highlight of the series is when he shows his true serious colors or fights – he is very strong physically and good at a brawl.
His counterpart is older and colder Danno, a high-level yakuza, who rose due to his strong personality and talent in accumulating dirty money. Danno is not a fighter and is referred as “yakuza intelligentsia”, outwardly he is a young entrepreneur, you’d see at a prestigious company. Danno is an interesting mix of good heart, coldness, that runs deeper than him playing the part of a thug, and dangerously strong fixation on revenge. Danno has class, which Ikuo lacks in any of his forms, exactly in the double the normal person’s amount. Unfortunately, Danno is always shown off, which gets annoying (the art is not quite there), and he plays fairy godmother to Ikuo – it’s like he has no other things to do. What Danno does for the yakuza is skimmed over too, but, well, at least, there is no glorification of the criminal lifestyle, or not much.

The other notable characters are the female prodigy partner of Inuo – Hibino, with her own set of troubles (second generation, a girl, partnered with the supposed idiot), though, unfortunately she gets sidelined a bit lately, and Chono, a detective so good, that he starts to suspect the two protags.

The art is decent. Some shots are “off-model”, Danno is unintentionally funny at times, and the female detective loses her nose a lot, but in the end the art carries the story well, it is detailed as it is necessary for a detective story, the characters are recognizable at all times. The quality doesn’t drop anywhere, and some panels are imaginative, I especially like it when silhouettes are superimposed on the scenery, as if in a night-time window – this gives off a tasty noire vibe.

(I should also point out the good quality of the available fan translation and the amazing margins comments by the team – guys, you’re good reader partners, thanks!)

To sum it up – if anything I’ve mentioned clicked with you, I advise to read this. There’re no serious downsides (like excessive violence, sexism or fanservice), and what I’ve described as silliness is nowhere near the level of what we see in many popular manga. And you know what? Awesome Danno is awesome, can’t do anything with it. Even if you’re not swayed by his or Ikuo’s charisma, deep underneath in Ouroboros you’ll find the heart of a proper police drama – questions of duty, justice, crossing the line, power and loneliness. The plot may start to drown in politics and over the top relationships, my current worry is that it is becoming too melodramatic, but it will get to another high-stakes high-tension shootout in the rainy night, there is no doubt. The pros severely outweigh the cons, seriously, so – hands up, this is grab and read.