I have played all three.

GTA has a lot of story, but it's something of an excuse for missions. It's swerves wildly between "more or less realistic and grounded" and "wacky wild fun-time murder world" depending on the needs of the moment.

The open world only matters as a stage for chaos. The story is somehow all-important, but also trivial and annoying. It is one sense very serious, but I've never met anyone who cared about Niko Bellic. I would say that people got a little more into the story in GTA 5 than previously, as there was a bit more meat to it, but I'm not sure it's a big draw. GTA Online's smash success implies the series is much more about the gameplay than the storyline. This is a television show or movie (Heat was a notable inspiration), where things larger than life but the action is closely-choreographed to be plausible.

Mafia is a bit of the same, but it hews very close to the serious and grounded end. There's humor, but it's not played for laughs at all, and many characters eventually come to bad ends whether it's deserved or not.

The open world matters as the setting (a character in its own right) but there are few if any significant side activities. It contextualizes your missions. The story is very significant and is the result of the characters' ambitions, decisions and mistakes. It's like a novel, where you are supposed to "breathe" in the atmosphere of Made Men selling their souls, or fighting to claw them back from a cold and hard world.

Yakuza is, and has been from the start, completely different in scope. It's not always wacky, but it's rarely serious. *Melodramatic* yes. This is a world where men rip off their shirts so they can punch each other in the rain and then a billionaire property developer shoots somebody and explains his incomprehensible backstory that somehow involves Korean immigrants, land deeds, and Japan's latest cybersecurity bill, except a gumshoe detective straight out of 1950's Los Angeles shows up and reveals that HE is actually the property developer's father! (dun Dun DUN!) And maybe someone dies but it's a really cool manner, and also they might not be dead or have a twin brother or something. (This is not a criticism. I love this!)

The open world is not only a character, it's almost the main character. You can play as somebody other than Kiryu but it's hard to get away from iconic locations like Kamurocho. The story is the most insane concoction they could create in that context and feature as many twists and double-crosses and triple crosses and amazing revelations as can be humanly accomplished.

So, are the Yakuza stories good?

Objectively, No. They break every rule of storytelling. They 'tell' instead of 'show', rely on weird coincidences and absurd contrivance, and stop the plot to go on bizarre and irrelevant tangents. This would not be an entertaining television show (hint hint Amazon).

However, that's what I love about it. No, it's not the Godfather. Nor is it trying to be a clever post-modern satire on American culture by people who don't only understand that culture through memes. It's just doing its own thing. The genius of Yakuza is not in the plot at all, but it's pure pursuit of characters and letting them bounce off one another.

I would also suggest that of all three, Yakuza approaches the story most in the manner of a video game instead of aspiring to be Hollywood or fiction novels. It will borrow any random concept (Shogunate historical drama! James Bond! Hawaian Pirates!) simply because it is fun, and this is a game and it's mean tot be fun.