Several thoughts:
Animorphs is immerisive, but nowhere near the levels of Harry Potter. Being based in the real world, for the most part, Animorphs, didn't need to spell out rules or make societies. But they also kept name, ages, locations, all hidden. Harry Potter give you back stories, genologies and other meaningless details for almost everyone and everything, which they kept coming back to.
On that note, the Harry Potter books tied together. There's only 7, but each is a part of the whole. We have another thread right now debating which books are skippable. It's a series, but most of the Animorphs books can be read independently and non-sequentially. It doesn't have that felling of involvement that which a character grow stepwise does.
Also being told from first person, Animorphs is more limited in story telling. You have to be there, or here it from someone who was. HP took you needed to be, you were an observer, first hand, not being told a story.
A large part of it was, I think, the films. And they were timed well. The first three are almost paired to the LOTR films, in the middle of the star wars prequels, it was a good time for fantasy film, which HP having that plus, by the way, this one stars kids. Kids relate to kids, and again, they worked to make it so you grow with the film characters. You have that audience, the ones that will grow into it, the ones that stay with it, and of course theirs some non-kid interest in wonder and adventure. The books were getting big before then of course, but we all know people who haven't read but have seen. And things like that grow the franchise, and the books are no longer the franchise alone. We'll never understand the effect of the books alone, because it had all this stuff going with it. ven if you started because of the films and wanted to learn the back stories though, you went to the books.
I know a number of people in teaching who give credit to HP for bringing reading back to a generation. At a time where ever room had a TV and console games weren't that expense, people-kids-didn't read for fun. But then this story came out that was getting big reviews, and getting a movie prepped, and teachers had copies, and it made kids feel good for reading something that was over 100 pages. In my mind, this might be the biggest thing. It (is credited to have) re-ignited an interest in reading. Everyone says reading is good, so if this is the thing you need to start people on to get them to read of things, everyone's gonna give it a try first, and because it is so condense and woven together, everyone has a stronger involvement. Saying Animorphs was the HP of it's time, even if true, is not as impress, because most kids weren't reading for fun (Everyone in my class was aware of Animorphs, but no one read them. Couple years later, same was true for HP, till the films, then they joined me there). If these teachers are right, it changed reading a popular book to reading something popular.
I like HP. My favorite books behind Animorphs. But I'll also say this, HP started to spike the same time Animorphs started to fall. I've admitted to dropping the series as a kid in the early thirties. At the same time, I was being encouraged to read HP (because at that time I only read Animorphs. Fun fact, it did not expand my desire to read more). So here's this series, that does have many aspects similar to Animorphs, but is new, and fresh and growing at a time Animorphs, story wise wasn't. If you're familar with Kenshin, it was a great anime that had a horrible filler arc that killed the show. Even though the source material could have given the series a great pick up, the damage was done. Animorphs was weak for over a year, and that's a long time to falter for a publication that comes out monthly.
tl;dr: World crafting, character growth, films, timing, literacy, proportional quality.