OH GAWD YES.
I find the books to be waaaay better than the movies, and I say that as someone who really, really likes the movies.
Note, I read the books as a mom, expecting a children's book, and some people I know who started reading the books expecting Literature were disappointed.
I was bowled over by the books though (just read the series for the first time last summer, at the same time as my kid).
There is just so much more detail in the books and what is amazing about them is that Rowling had the entire plot mapped out before she began the first one. So there are foreshadowings, yes, and also details that seem throw-away minor (so that the movies didn't include them) that then become very important later on.
Rowling evidently had a sit-down with Alan Rickman before the first movie to explain that Snape needed to have some character shadings, he wasn't necessarily all evil. (How did you like the flashbacks in HP7 pt 2 btw? I thought that was awesome. Anyway.) The first movie came out before the last books were out (at book 4 or so?) so the world didn't know yet that Snape would emerge as, in some ways, the hero of the books, but Rickman knew (if only in abstract).
But Rowling couldn't do that for the thousands (probably literally) of details that end up paying off in some way down the line (like SPEW). (I'll leave SPEW for you to discover.
Just as a tiny example that I can remember now, Harry actually sees the diadem in the room of requirement when he's hiding something, in an earlier book ("Half-Blood Prince," I think, when he's hiding the Half-Blood Prince's textbook from Snape.) He just has no idea that it's important. So there's this little gasp moment as you (the reader, if you've retained all this info!) realize exactly where the diadem is, at about the same time Harry does.
That's what Rowling is GENIUS at in the books, that I haven't seen to the same extent in the movies. Hints, information that is THERE but you have to think about it, and then the thrilling CLICK as you get it.
As one more example, in the movie Snape out and says "you have your mother's eyes," in the book it's just "Look... at... me..." (conk), and it's not until the next chapter, when Harry views Snape's memories, that we put all of the "Harry has his mothers' eyes" comments into context. (And in the books, Harry is always being told how much his bright green
(ahem, movie) eyes are like his mother's, to the point where he's sick of it.) Those dots are never explicitly connected, you just have this "OH" moment.
Since you know how it turns out you won't get the full benefit of all of those, but I bet there will be a lot of them anyway, even if in reverse (i.e. when the info first comes up, rather than at the payoff).