Compare the lives of when they live under Jones and Napoleon. In what ways has Napoleon himself proven himself a similar tyrant?
To answer this question, let us look first at what life was like for the animals under Mr. Jones. According to Old Major's speech in Chapter One, the animals were never allowed to enjoy their own produce, they worked every day, were subjected to violence, and sent to slaughter when they were no longer useful.
Comparing this to life under Napoleon, we see very few differences. Napoleon uses his guard dogs, for example, to inflict even bloodier levels of violence. Moreover, an animal is not allowed enjoy a retirement, as we see when Boxer is sent off to a glue manufacturer. Similarly, the animals are not allowed to enjoy their produce, as shown by Napoleon's unfair distribution of the food rations.
Like Mr. Jones, then, Napoleon uses similar methods to promote inequality on the farm and to maintain his absolute power. Through his control of food and his use of violence, alongside the threat of being sent to the "knackers," Napoleon has become ever more tyrannical than his human predecessor.
Essentially, the animals' lives under Napoleon's tyrannical reign are equally as miserable as they were under Jones's authority. Napoleon suppresses the animals' individual freedoms by making them work extremely long hours and does not provide a sufficient amount of food for them to eat. Under Napoleon's rule, the animals live in constant fear of his wrath and struggle to survive each day. Napoleon manipulates the animals through propaganda and lies, which is somewhat different from how Jones controlled Manor Farm. Even though none of the animals starve to death, Napoleon does orchestrate brutal purges by slaughtering dissidents in front of the other animals. Napoleon's violence and purposeful negligence are politically motivated, while Jones's abuse was a result of his alcoholism and malevolent nature. In both cases, the animals served their masters, whether it was Jones or Napoleon.
The way that the animals live under Napoleon is essentially no different than the way they lived under Jones. There is only one real difference that I see -- no animals are killed for food under Napoleon (although Boxer is killed for money, but at least it is after he is already pretty close to death).
Under Napoleon, the animals have little choice in what happens to them. They have to do what Napoleon says or they will die. The same was true under Jones. To me, this means that little has changed.
Napoleon is similar to Jones because he is using the animals' work to make a comfortable life for himself. He cares mainly about himself (and the pigs) and does not care if he is being fair to the other animals.
The previous post is essentially correct that little changes on the farm except for the fact that the animals are not killed and eaten. However, animals are killed--not for food, but for political purposes and, in Boxer's case, for money. However, the animals (the non-pigs, anyway) eventually work harder and longer hours during Napoleon's rule than under Mr. Jones. Their rations also eventually diminished to a smaller amount than when they were fed by Jones (or at least when he remembered to feed them). Of course, the animals were told differently by the pigs, so they weren't really sure if they were getting less food or not; they do know they were hungry, however.