I'm on chapter 2 in Judgment. Chapter 1 is very linear, it has no side cases at all, everything is main story. Once you get to chapter 2 the game opens up and you get the side content you expect from a Yakuza game (this isn't technically a Yakuza game, but for all intents and purposes it's a Yakuza game).
The story is great so far, but that was never in question. Ryu Ga Gotoku are, and have always been, great at storytelling. The writing is great, the characters, whether prominent or obscure, all have personality, the pacing is spot on. These folks know how to tell a story. I can also happily confirm that the English translation and voice acting in this game is top-notch. SEGA and Ryu Ga Gotoku have put more effort into the western localization than any previous title and hopefully it sells like hotcakes in the west because this level of effort is appreciated. So whether you go with Japanese voice with English subtitles or English voice, you're going to get a premium experience.
There are also some quality of life improvements over Yakuza. For example, you no longer have to keep holding X to sprint, you can just press it once and Yagami will keep sprinting as long as you keep moving. Also, I like the combat in this game better than Yakuza. I'm not sure how to explain it, but it seems to flow a little better. Also, you can do attacks jumping off walls, which is all types of rad, though I need to work a lot on my aim with those attacks. Another small improvement is that you no longer trigger a cutscene for most fights (you do for boss fights). When you run into common mooks on the street you fight them right there on the street without a break in gameplay. In Yakuza games you fought them in, for all intents and purposes, an instance. I like how the bystanders react when a fight breaks out. Some flee, some stand around and cheer on the fight, and some film it on their phones, in landscape mode, of course, because people in Japan aren't disgusting degenerates.
On the negative side, it looks like there's no karaoke mini-game.
I get they had to remove some mini-games since they added some new ones, but of all the mini-games to remove, why karaoke? It's arguably the most popular mini-game in the Yakuza games.