More content, better combat (muuuuuuuuuuuuuuuuuuuuuuuuch better combat). Problem with 6 is they decided to move to an awesome looking new engine for the game. Which always means less content. For Kiryu's last game... not the brightest move, should have done a side story that year and released 6 a year later with more dev time.
6 has probably the smallest number of unique heat moves since Yakuza 1 (I should probably fact check that). Weapons? Knife, Gun and hammer only, anything else is cut. Can't buy weapons either as Kamiyama's weapons shop is unreachable in this game (they cut the top of the map - the hotel district, purgatory and that whole top section (its all added back into Kiwami 2 though). On top of that while some awesome new heat moves are added others are removed.
Also, Kiryu's move list shrinks enormously from both Yakuza 5 and 0 (both had different moves lists for KIryu, but super fleshed out). All Komaki counters bar the tiger drop are cut, and the TD itself is neutered in its performance as the window is tighter and its damage is drastically reduced. You do get the extreme heat mode which does add some cool new finishers in, and its incredibly useful in its own right but it doesn't compensate for the number of moves Kiryu forgets between 5 and 6.
Content wise its a bit weird. Side story number is reduced compared to most Yakuza games, while 5 has a lowish number compared to previous games (around 75 instead of 100+) each of those stories are fairly involved, plus 4/5 characters also have huge "Another Drama" modes that give them another big plot to deal with (so all told its fairly even in side story total if you take these into account to previous games).
6 only has around 50 side stories, and several of those are basically short intros to the main mini games to the game.
Which to be fair is one thing 6 shines on - the mini games are a mix of old (Mahjong) and new (super fleshed out arcade, Rizap fitness training, Snack Bar conversations, Spear Fishing, Baseball league, Clan Creator) with several other mini games getting new gameplay such as Hostess club (more of a strange card battler now), darts (completely different, easier control scheme), Karaoke (note charts now displayed in a more readable way - one straight line instead of random rows) etc.
A few mini games are cut though - bowling and pool are gone and have never, ever returned in the series to date, Shogi (back in Kiwami 2), gambling games (back in Kiwami 2/Judgment), UFO Catcher Crane game (Kiwami 2)... basically they axed a few legacy mini games to focus on new stuff while then bringing most back in subsequent games - for example Shogi in Judgment has evolved into something pretty cool with a brand new challenge mode to clear, its best incarnation ever.
Don't get me wrong though, 6 still rocks as a game. Less can be seen as more side story wise as they are all fully voiced (only game to do so) and the actual quality of the stories in these are among the best ever, some really funny, touching and... Ono Michio in execution. Plus a few amazing call backs to previous characters/games (especially 0/Kiwami). The new mini games are almost all excellent, with the arcade getting playable Virtua Fighter 5S (best mini game ever) and the actual main story plot and characters being top 3 easy for me, its incredible. Oh, and its soundtrack, second city and set pieces are all fantastic as well.
Judgment basically just then benefits from longer dev time and a more mature engine. More mini games (almost all arcade games from 6 returns alongside several new ones and the UFO catcher is brought back), Gambling is fully back, combat adds in loads of heat moves both old and tons of brand new, weapon variety... eh that's kinda tied with 6 as Yagami is a good boy and won't acquire illegal weapons so you can really only find around 3 types hidden in the city (Kiwami 2 though fully adds all the crazy weapons back into the game with Kamiyama), you get two stances worth of moves for Yagami, including some badass wall based attacks, the city is fully accessible with several new places to enter, new mini games alongside old ones (only casualty is Karaoke which is cut in Judgment due to Sega not paying the actor to sing, on account he's a famous pop star in Japan and it'd cost extra). There's also 100 side stories in the game - 50 larger side cases (many hilarious) and 50 smaller friend events where you befriend the weird and wonderful people of Kamurocho. And its secret boss is among the best in the series for me.
You really can't go wrong with either, but Judgment is definitely the better of the two for me just thanks to having more time put into it.
