In the world of 'Harry Potter' book-to-screen adaptations, I tended to find this particular chapter one of the weakest (it's a close one between this and 'Deathly Hallows Part 1'). Where the book opens up some fascinating perspectives, the movie kinda just dances around some of them. But don't get me wrong. The movie does manage to nail a few things.
Now that Voldemort has returned to power, things are bleak in the wizarding world. A further danger is more clearly illustrated here as well, as the Death Eaters (Voldemort's followers) have broken the barrier between the wizarding and muggle world as well. One such scene involves the collapse of a bridge - one of the very few things the movie did better than the book, as the book tells the bridge collapse as a news article.
The sixth year goes ahead as planned, but with fair warnings for the dark times ahead. Snape (Alan Rickman) finally gets his position as the Defense Against the Dark Arts teacher. Replacing him as Potions teacher, is Professor Slughhorn (Jim Broadbent) - a man who Dumbledore (Michael Gambon) must have at the school this year. Slughorn has a fondness for meeting the most interesting wizards of the world, and Dumbledore needs Harry to persuade Slughorn to give up a very important memory for the pensieve (an sort of basin in which wizards can store memories and refer to them later if the mind gets overwhelmed); one that could be the key to destroying Voldemort once and for all. In the meantime, Dumbledore takes Harry into the pensieve in order to study what Voldemort was like growing up, so Harry can have a better understanding of how he works.
Unfortunately, for the movie, the most intriguing parts of the story having to do with Voldemort's past are barely there. Instead, it focuses heavier on developing the characters' love interests. This whole idea was in the book as well, but it's kinda what I would consider the "filler" part of the book. That's the part of the book that side-steps the actual adventure to talk about something else going on in the meantime - although perhaps often crucial to the story. But this was more about getting Ron and Hermione set up to be an item as well as, more obviously, Harry and Ginny. And the real bugger of it all is that I swear there was more going on with Harry and Ginny in the movie than there ever was in the book. It meanwhile, as I say, sidesteps more interesting things but instead casually mentions them. For example Morvolo Gaunt's ring. Oh, you don't know who Morvolo Gaunt is? He was Voldemort's grandfather. There's a whole history there. But in the movie, I believe Dumbledore even says it's "his grandmother's", and it's responsible for his strange, new, blackened hand.
The movie isn't without it's charm, and it does manage to get a few things spot on. It really could have been the best of the movies if it was to focus more on the right things. But again, just all the lovey-dovey stuff seemed to overshadow what was more important. I gave the movie high praise in the beginning, but upon re-reading and re-watching, I recommend definitely sticking to the book. I know it seems obvious that the book is better, but this is by a long shot.
COMPARING THE BOOK
I guess I've gotten the gaping part of it out of the way already. Too much focus in the movie on relationships and the kids maturing, not enough focus on Voldemort's past. I don't wanna end up sounding too much like a broken record here, which I'm sure I may already be doing. Much like with 'Order of the Phoenix', we could be here all day talking about how much MORE is seen in pensieve, in the book. So what other differences are held in the book that didn't make the movie?
Well, as we know, the wizarding world is now getting exposed to the Muggle world, as the Death Eaters are tending to Voldemort's uprising. With this, in the book, there's a pretty entertaining meeting between the now former Minister for Magic, Cornelious Fudge, and the Prime Minister of Britain. This chapter provided an interesting explanation of how disasters happening in the muggle world were actually tied in with dark magic. Fudge explains to him that a new wizarding war is on the horizon, and it just would have been a neat before-title sequence. But I digress. The movie DID do a pretty cool job in just showing it all happen, and they DO say "show, don't tell". So I'm not exactly hurt that the scene is missing, but it would have been neat to see.
For starters, the opening of the book is far more entertaining as Dumbledore actually comes and gets Harry from the Dursleys. That's an interaction I'd have loved to see on screen, I mean, it would have meant Dumbledore finally coming along and putting the Dursleys in their place after all the crap they've given Harry. It would have been a good send-off for those characters, and they wouldn't have had to do anything to change 'Deathly Hallows Part 1' as they are only really in it to say goodbye to Harry.
Once at the Burrow, Harry has far more interaction with various members of the Order of the Phoenix. It's better explained that Tonks and Lupin are an item, and it would have set up Fleur and Bill's wedding better. The movie-going audience only just sees the wedding happen randomly at the beginning of 'Deathly Hallows Part 1'.
Getting to the Half-Blood Prince, did you notice how my movie review didn't mention it? It takes such a back seat in the movie, it's kinda ridiculous. This is mostly in reference to the text book Harry gets in his potions class. The book was written in with replacement instructions all over it. These instructions help Harry essentially cheat at his potions classes; a subject he typically didn't do great at. The movie does manage to cover the basics here, but a lot of the rest of this part was thrown into a bit of a montage.
It's admittedly a bit baffling to me that Rufus Scrimgeur had no part in the movie. After the end of 'Order of the Phoenix', Fudge loses his job as Minister for Magic, and Scrimgeur replaces him. It's not a big chunk of the book or anything, but he's always trying to get to Harry. Now that Harry has become ultimately famous in the wizarding world, Scrimgeur wants him to provide statements in favor of the Ministry, even after all they put Harry through the previous year - including hiring Deloris Umbridge, perhaps the biggest villain here who isn't Voldemort. The big instance happens at Christmas at the Burrow, but instead, the movie replaced it with a Death Eater attack. That scene got to a lot of people, but I believe it's the movie throwing us a bone of sorts. The Death Eaters have to feel like a real threat in this story, so without the scene, there's not that foreboding sense of danger.
Did any movie-goers wonder what the hell happened to Aragog in the movie? Did you notice that Harry didn't seem taken aback at all? I guess it could be argued that the Felix Felicis was just doing it's thing. But it is a topic explored more deeply in the book. All it would have taken was a little scene involving the trio going to Hagrids, and Hagrid explaining that Aragog was sick.
Finally, the one that bothers me the most is that final scene in the movie. Without spoiling too much (as if you don't know the situation thanks to the internet already) Harry chases someone through Hogwarts, and in the background there's a bit of a mini war going on between the students and Death Eaters. In the movie, it's just done almost too casually.
To finally close this off, I'll just make this one thing perfectly clear. Are the books better than the movies? Yes, generally speaking. But the movies do tend to have a certain charm of their own. However in 'The Half-Blood Prince's case, seriously, just stick with the book. It's far more entertaining, there's more going on, and it doesn't get so lovey-dovey.