I'm absolutely sure that this will sound condescending, but it is what it is...
The thirteen year wait between II and III means that the biggest change between II and III is likely to be you yourself. Inevitably you were a different person when you played II than you are now playing III — all the more so if you were a kid when you played II. This is a massive factor for everyone, except perhaps those who begun more recently with the remixes.
Related to this is the hype factor. If you allow yourself to get too hyped for something, it becomes impossible for it to live up to your expectations, thus all but guaranteeing a bad experience. This is the danger of hype, and the only way to avoid it is to try to avoid getting over excited before release. Easier said than done, I know.
Next up, I see an awful lot of people comparing KHIII to KHII, and especially to KHII Final Mix. I also see many people pointing out the unfairness of this comparison, since the original release (in Japan) was also lacking in all the Final Mix-style additions and post-game content. I agree with this, and I feel that people expecting Final Mix-style additions from the outset are misunderstanding how the video game industry works, assuming that it has changed fundamentally in the intervening thirteen years, when in fact much of it remains the same. Crucially, they still have to finish a game on schedule, and just because it seems to us like they've had forever to do it doesn't actually mean they had tons of free time to add extra content.
But that's not my point. My point is that the comparison with KHII is flawed because really the comparison should be with Dream Drop Distance. I'd argue that at this stage the numbers really don't mean much anymore — clearly DDD was a major entry to the story plot-wise (as was Birth by Sleep before it). III was also made by the same team that was behind these two games, wasn't it? All of this adds up to say: if you played DDD, with its ludicrously compressed story, which only really started in the final world, you should have been more than well enough prepared for KHIII's story — which actually isn't quite as bad as DDD's pacing-wise, as it does have lead-up throughout the game, even if it's just a series of cut scenes.
Comparison with DDD seems to me to be far more enlightening. In fact, it might not even be going too far to say that we are in fact stir waiting for the spiritual successor to II, because III feels much more like the successor to BbS and DDD.
Most of the other problems people raise about KHIII don't impress me much. I've never cared about difficulty — I'd rather it was too easy than too hard any day. That's not why I play these games, never has been. Complaints about the Disney worlds invariably apply to previous games too — because let's face it the stories here have never been the strong point of the game. I've seen people laud KH's worlds over III's, but I just don't see this at all. On the contrary, I think III's are nothing more than a continued refinement of the formulas established in previous games, with similar results — some worlds work great, others not so much, but all end up being fun if you let them.
Even Arendelle had its charms, and frankly we've already seen the back-and-forth design way back in KH's Deep Jungle, which had the exact same "sending you there and back again" feeling.
The bottom line is that, objectively, KHIII is exactly what it was expected to be: another solid entry in the series, mostly using all the same formulas, adopting bits and pieces from throughout the series. Details aside, how could it have been anything else?