While Paulie_D already gives a very good answer right from the director himself, after having seen the film we can take a closer look at its story1, be it only to pretty much confirm what Villeneuve says, that
it's ambiguous and ultimately unimportant (i.e. all versions).
Let's first take a look at what the most significant differences are, the ones relevant to the sequel. As you said, we on the one hand have the different endings and on the other hand the much more ambiguous question of Deckard possibly being a replicant himself. I'll try to hide specific story elements about the new film behind spoilers blocks, seeing that the likely audience of this question are people who haven't seen 2049, but of course we won't get around discussing its broader themes.
Let's first take a look at the ending. The original theatrical version featured a rather happy ending where Deckard and Rachael drive through a beautiful countryside elaborating on the fact that Rachael might live longer than the normal 4 years of a Nexus 6 model. However, it's still unclear from Deckard's voice-over how long and nothing prevents her from dying a natural cause afterall:
Gaff had been there, and let her live. Four years, he figured. He was wrong. Tyrell had told me Rachael was special: no termination date. I didn't know how long we had together, who does?
And while the primary difference between the two endings is more of a tonal nature, from a plot-based point of view nothing really precludes the theatrical ending still happening after the director's cut one, but just not being shown. And while it presents an environment far different from the rest of the film (and taking some of its dystopian and dismal atmosphere from it), as we learn from 2049, the world might not have been a complete disaster by the 2010s yet (when it alludes to the collapse of the ecosystem in the 2020s).
If we look at the tone alone, the director's cut is a little less optimistic and more ambiguous about their future. And indeed, it wasn't all happy-go-lucky for Deckard and Rachael after leaving the city, but it wasn't all terrible either and they first and foremost did make it out of the city alive afterall.
While they seemingly had to go into hiding, especially after the birth of their daughter, they did have their time together, even if a short time and ultimately shared the wonder of birth with eachother, even if that was of a short duration. And while Rachael does indeed die not too long afterwards, it's IMHO not entirely clear why. It could have been birth complications as well as a replicant timeout.
So you could say tonally it might be nearer to the ambiguity of the director's cut, but story-wise it doesn't make much of a difference.
Now the bigger question if Deckard is a replicant or not. While the director's cut hints at this possibility, it's still largely ambiguous. The biggest point is that we're considering it, and that's what makes it interesting, not necessarily the clear answer to it (even if both Ridley Scott and Harrison Ford claim to have their own clear answers to it). And you might be delighted to hear that the new movie doesn't answer that question either. In fact, it seems to dillute it even further by extending the things replicants are able to do,
by having Rachael (who clearly is a replicant) have a child with Deckard. If she can procreate with a human, she might as well be able to do so with another replicant.
This on the one hand makes it more likely for someone to actually be a replicant by reducing the things that differenciate them from humans, but also makes the question more difficult to answer (and ultimately irrelevant, reducing it to an entirely bureaucratic technicality).
Especially with the possibility of replicants having children, which is prominently used as a sign of their elevation beyond replicancy(?) in the movie. Is a replicant that's not made in a laboratory/factory but a womb still a replicant? If yes, then why?
And while the film still doesn't give an answer about Deckard's very own nature, it still keeps it ambiguous and leaves the possibility of him being a replicant open.
While he obviously lives longer than a few years, we've seen later Nexus 8 models like Sapper do that too. And there is one specific scene during the ending when Deckard is in Wallace's office that explicitly picks up this idea, where Wallace hints at the possibility of Deckard having been specifically manufactured and set up to fall in love with Rachael for this very purpose of evolving replicant procreation. This is countered by Deckard claiming that he "knows who he is" (whatever that means). However, this seems more Wallace grabbing for straws and playing mind-games with Deckard than any genuine knowledge about the past and Tyrell's plans, especially after the blackout.
So to sum it up, it is really a sequel to both major versions, with a story being able to fit both and a tone and ambiguity setting it somewhere between the two. And this way it also doesn't give us the easy answer to what interpretation is the ultimate truth, since they all work and are probably up to us. We can believe Ridley or Harrison, or make up our own mind, possibly with the additional help from 2049, which doesn't seem to favour nor preclude any interpretation, but if anything makes the difference even more moot and shows us yet again that the question is more important than its answer.
1) And even if it is less based on interviews, it still tries to reason by the very movie itself and is thus not too much speculation. See it as an addition to Villeneuve's answer, solidfying it by specific proof from the film itself, so you know he didn't talk nonsense in his interview. ;-)