I'm not a huge fan of the mandatory mini-game sequences (I don't really like mini-games most of the time, though this is a YMMV thing and not an "it's objectively bad" thing, I'm sure a lot of people like it). I think the open world stuff was not great. The pacing is a mess just like the previous installment, a natural consequence of chopping a game up into 3 games.
Some of the changes to the story feel like sanitation: making it so Dyne doesn't threaten to kill Marlene and he doesn't commit suicide and they don't cover the belief that neither Dyne nor Barret deserve to hold Marlene because of the blood on their hands, making Cait Sith's betrayal less of a betrayal and he doesn't threaten Marlene (running theme here, huh), making Cid way less abrasive to the point where he feels like a different character entirely... oh, and while I liked the Gi sequence, it felt like it was awkwardly squashed into the Seto scene, I think that could have been executed better in a way that didn't mess with Nanaki's revelation about Seto. Also, wtf happened to the Tiny Bronco? Did I miss something? That was so weird.
Then in the late-game, the changes to the Temple of the Ancients were weird (why can the Cetra talk to everyone and not just Aerith?!) and then there's that bizarre sequence where Barret chucks the black materia, Cloud gets it back, then Aerith takes it from Cloud, then Cloud takes it from Aerith, then Cloud gives it to Sephiroth, and it's like... why? In the original Cloud loses complete control of himself and starts attacking Aerith, which is why she leaves; she knows he can't be trusted not to be violent with her again.
And then the whole ending sequence, yeesh. They seemed absolutely determined to suck all the weight out of that sequence, and again, they sanitized it, not showing the rather horrifying stabbing and withdrawing of the sword. There's stupid-ass ghosts obscuring everything and the game decides to insert a bunch of rule-of-cool multiverse fights... and we don't even see her being laid to rest.
Most of the above listed changes feel like they add nothing of value and are an active detriment in many respects. It's odd because when they nail things they really do nail them. There were a lot of story tweaks I really liked, some great details added and a lot of awkward parts of the original made better. A couple of examples: I liked how they introduced Yuffie to the party, they made a head-canon of mine regarding Nanaki full-on canon, I liked that they had little sequences with Reeve and made it so that he looked up Vincent as soon as they ran into him because Reeve's presence is sorely lacking during this arc of the story, it was a good idea to put those in. I think they did a good job of implementing Tifa and Cloud's complicated dynamic alongside the changes to the story in general. I liked the Gi sequence even though it was a bit awkwardly inserted. The Junon sequence was really entertaining even if it's really strange that no one recognizes the party as the terrorists prior to nabbing their disguises or after discarding them on the ship, it's a minor gripe that doesn't change the fact that the sequence was improved noticeably. In a way that makes the parts I don't like more disappointing, if that makes any sense. The multiverse stuff... people justify it by saying it's obviously going to pay off in the third installment and, sure, that's a possibility, but these games also do actually have to stand on their own, and in Rebirth, the multiverse content really hurts the late-game in particular. Zack literally contributed nothing worth noting to Rebirth at all.
Edit: Also I don't see the point in wasting time quibbling over whether it's a remake or a sequel. That's a very strange thing to get hung up on. Call it whatever you want. Who cares?