Why do the animals suffer in "Animal Farm"? Is it because of Napoleon's behavior or their own weaknesses?

Very good question. 

 In reality, neither are the primary cause for the animal's suffering in the story.  While Napoleon has obviously molded himself into a tyrant worse than any human the animals have dealt with before their revolution, alot of the problems are only allowed to continue do to the animal's own weaknesses.  Granted the attack dogs are a deterrent, but they've dealt with armed farmers, what had stopped them from rising up again?  Boxer's death should've been the most obvious wake up call.  

For example, take the charactere Benjamin.  He's lived a long time, and its no secret that he takes no sort of enthusiasm from any promises made by either Snowball or Napoleon.  Unlike alot of the other animals, he has an insight that allows him to think outside of the 'herd'.  The chapter with Boxer's departure is the first time he ever really does anything close to disent, yet he's known the whole time pretty much what the pigs are up to.  Its his own stubborness that keeps him from reading the changing commandments when he is one of the few who can read as well.

You also have more naive characters like Boxer and Clover, who really want whats best for the farm, and are the very sort of hard working people someone can manipulate.  The sheep don't think for themselves, and its almost as if the animals are in denial, which could be way they so easily dismiss their own suspicions.  

So I would say it would be both.