So here is the inevitable compare/contrast of book to movie.
I will always admit that taken anything from the page to the screen (being either movie or TV) there will always be something lost, however in that they do have the advantage of telling a story within this universe that has been established. Sadly this rarely happens. Anyway!
The first issue is one of speed. In the book it too many years for the zombie threat to become known to the general public, since the plague originated in China, the Chinese government had to mobilize its armed forces but had to create a false impression as to why (masking their general health and safety sweeps to nearly invading Thailand). Intelligence was a huge factor and even with the processing power of the NSA or CIA combined there was too much going on in the world for people to take notice let alone take seriously of the threat that was building.
The Movie on the other hand takes a Dawn of the Dead 2004 approach where everything happens way to quickly, there is very little time to react to the threat which does mimic some form of tension but it makes the objective of the main character obsolete within the first 10 minutes. The idea of finding patient zero is unreachable from the get go, since there is a huge mass and you don't know any method detection without a huge selection of medical means, which they clearly do not have. Brad Pitt is only really the leader or has relevance because of default, such as the plot demands it to people accidentally killing themselves.
Side note. Basically this movie is huge on the contrivance or as I call it, the God hand. The scene in the beginning shows the directors incompetence in the matter of going from scene A to scene B, there was no need to the garbage truck to literally appear out of now where (like God placed it down and said, now Brad Pitt you can progress in the story!) to the Soldiers who didn't instantly blow his bloody brains out when he charged a military check point (seriously in that situation he would of been dead, the soldiers went weapons free).
PS the Israel part was full retard. Full. Bloody. Retard.
The zombies. Now this isn't a case of slow versus fast but again on what the book did to the movie.
In the book the zombies were slow 'shambler' types, the virus or whatever infecting them was an unknown type, the media in the book (from the government and other sources) to mask the truth state that it is a new strain of rabies and a drug was developed (specifically for rabies) for this giving a false sense of hope and protection. Time from infected to reanimated took several days.
Now the movie sort of declares this is a form of rabies. Again it shows how they didn't clearly read through the book, they just cherry picked words and discarded the rest. The incubation period went from a literal twelve seconds (there was even a timer) to "Oh wait it can take several days" it is mind blowing how even in their own fantasy world they can't keep consistency.
How we succeed.
In the book it is matter of us coming to terms with the threat and nearly losing it all, its only through human ingenuity (The Redekar plan) and determination do we succeed in gaining victories against the zombies. The issue raised is in how we fight wars, all of our gear and technology is opposed to fighting one threat, humans when faced with a zombie (en mass) most of that is redundant. The battle of Yonkers shows how both unprepared the US Military was but also in the nature of soldiers training (aiming for center mass) coupled with stupid higher up command decisions.
The movie doesn't take anything of this sense, instead it simply has a David 'I'm a retard' Lindelof type endings in which he clearly doesn't understand anything of subject matter viruses or even basic high school genetics/biology.
So overall (though this is a condensed version) the movie as said before is an in name only, the fact that this planned out as a trilogy is laughable at best. If you remove the title, the incompetence of the director and the utter dire dialogue and wooden acting you can (after several drinks and a night out with Bruce dressed as a pokemon) see this as a 'what if the rage virus escaped England and infected the world' sort of thing. Rated PG-13.