I'm a recent Yakuza convert. 0 was my first and now I love the series
Now that I'm finally playing Shenmue, the whole "Yakuza is a better/evolved Shenmue" thing is just utterly baffling. The games couldn't be more different. It's like saying Fallout 3 is a better STALKER because they're both post-apocalyptic and have guns
Yakuza is a JRPG-esque brawler with copious amounts of combat, with insane over-the-top moments that somehow work perfectly with the emotional yakuza drama. It's fast and frenetic and flashy and everything revolves around fighting.
Shenmue is slow and sedate, a 3D visual novel/adventure game that occasionally has some combat, but is more concerned about letting you meander around town and being a slice-of-life proto-immersive sim.
The only similarities that Yakuza and Shenmue share is that they're story driven and that they happen in lively atmospheric sandboxes. Beyond that, the games are nothing alike. I don't get this continued insistence that Yakuza and Shenmue are so similar because they aren't, at all. They're practically in entirely different genres, their pace and gameplay and designs are so different
A lot of the comparisons are a bit of a holdover from the reveal of the original Yakuza, which made the game look a lot more like a modern-day PS2 Shenmue than it ended up being. Even so, there is plenty of Shenmue (mostly 2) DNA in the Yakuza series even if they're not necessarily all that similar, especially after the inclusion of more traditionally Japanese-looking settings like Onomichi in Yakuza 6 or Ryukyu in Yakuza 3.