There's really only a few changes I would make if I had my AAA big budget Shenmue III. I'm not gonna say Story or Plot because its too obvious and everyone here is no doubt going to mention that. Yes, I wish SIII had more story but again, it's such an obvious criticism that I'm not gonna mention it.
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The Graphics -- Or more specifically the animations. I quite like the look of Shenmue III in general but some of the character models could have done with more polish. That and the animations. I think the animations in general could have been a little less...stiff.
The Fighting System -- if we had all the money in the world to throw at this then I would have paid SEGA whatever they wanted just to get the core fighting system back. I didn't mind SIII's system for what it was, but given the choice? I'd gladly pay SEGA to get the old fighting engine back. Or further refine what they had for SIII by polishing the animations, adding throws and true counters and such. It has potential, it just needed more resources thrown towards it.
The Affinity System Done On A Full Scale -- The most promising thing about Shenmue III pre-launch was the hype around the affinity system. It's kind of there in Shenmue III with regards to Shenhua, but the way they made it sound pre-launch was that it was going to play a bigger role across the game in general. That people in Bailu would react differently to you if you were out without Shenhua and such. I think bits and pieces of it made it into SIII, but the way Yu was talking about it pre-launch, it seemed to be bigger than it actually was. So I'd like to see that system fully realized.
More Dynamic QTES -- One of the things that impressed me about Shenmue and more so Shenmue II was the branching QTES...that the scenes would play out slightly differently depending on how many hits or misses you had. I missed that and thought the QTES were somewhat lacking in SIII in that regard. So if I had my ultra budget Shenmue III, that's something I would want back in.
AM2 Arcade Games -- Chobu Fighter was nice and all but I did kind of miss Space Harrier and Outrun in the arcade. Pay SEGA to get those back in given my ultra budget Shenmue III.
Darts -- I really missed Darts more than I thought. Again, the mini games in SIII were nice and all, but I did kind of miss Darts.
The Tape Recorder - I'm one of those people that missed the tape recorder in Shenmue II and was always hoping it would make a return in Shenmue III someday, but alas....why did they get rid of the tape recorder in Shenmue II anyways?
Something akin to Social Links with some of the NPC's -- One of my favorite random things about Shenmue II was the way in which you could talk to Fang Mei and over time your friendship would subtly grow to the point where the more you talked to her, she actually would start addressing by his first name showing a sign of a bond being formed. It's such a small detail, but I really liked it and it encouraged further interaction with her without shoving a meter in your face. That's kind of more what I wanted in Shenmue III.
More evolution with the NPC interactions on a level we haven't seen before in a Shenmue game. Something like a Social Link system but not shoved in your face. Something where you actually have to naturally engage with NPCs and build up a relationship over time by simply talking to them over and over. I guess something akin to what I thought the Affinity system should have been.
Baisha -- I'm sure even Yu regrets not being able to fully realize this in SIII. So yeah, this is one thing I would like to see in my dream AAA open cheque Shenmue III.