Orwell uses various elements to convey the differences and similarities to Jones' control and that of Napoleon. When Jones ran the farm, the animals were mere slaves, there to do their master's bidding and to feed his greed. To ensure his comfort. The animals were regarded as property and treated as such. They worked themselves to death, literally. When their usefulness was over, they were either brutally slaughtered or sold. There was no provision for retirement. No animal lived a full life. Life was hard and laborious, except of course, for Mr Jones' favourites: Old Major, Mollie, Moses. They served another purpose, however.
Although the lives of the animals devolve into typically the same situation as in Jones' time, there are differences. The animals do not feel the need to rebel against the tyrannical control exercised by Napoleon. Essentially, they are, on the whole, apathetic, best illustrated by Benjamin's refusal to either agree or disagree. Even though there are periods of protest, these are soon suppressed by Napoleon's swift and brutal retribution in which he uses the dogs to tear out the throats of those who have 'betrayed' him, or starving to death those who have disobeyed his instructions (the hens who refuse to give up their eggs for sale).
The animals meekly accept Napoleon's rule for various reasons: Firstly, it is better to be treated in this manner by their own kind, rather than by a grudging human. They are loyal and will sacrifice everything to display that. What a noble act! Secondly, they believe that whatever is done is executed in their best interest. Squealer, through his propaganda and misinformation, makes sure that they understand that. Thirdly, the animals are terribly afraid. The threat of the dogs tearing out their throats, after they have witnessed these atrocities, drive them into submission. Also, there is the constant threat that, "Jones would come back." In the fourth place, the animals are naive, gullible, uneducated and generally unintelligent.
They cannot remember, and this fact is grandly exploited by Napoleon whenever he has Squealer change the commandments. The animals trust that the pigs know better since they are, after all, more intelligent. This clearly indicates that the other animals feel incompetent and they therefore lack the confidence to challenge either Napoleon or any other pig.
Furthermore, Napoleon introduces a militaristic system on the farm. Animals have to report for duty at specific times and on specific days. They have to stand to attention. It becomes their duty to celebrate specific events and to address Napoleon as 'leader'. This, in itself stifles any individualistic tendencies or the expression of free thought. The animals are kept in a constant state of exhaustion, which, in itself, discourages any desire to rebel or even think. It is hard enough for the animals to perform all that labour and to think will require more effort which very few of them are capable of, after all.
Another aspect one should consider is Boxer's almost unyielding loyalty to Napoleon and the farm. The other animals find inspiration in his maxims: 'I will work harder' and 'Napoleon is always right'. In his simple-minded way, Boxer thinks that he is doing good, but ironically, his loyalty unequivocally encourages the other animals to accept their exploitation as being 'for the greater good.'
So, in conclusion, one can therefore say that the conditions on the farm are far worse than they could have been at any time during Jones' reign. The animals have been suckered into accepting a totalitarian system because they believe that they are been better off than before. What a terribly disastrous and tragic irony!
One specific way in which Orwell compares the farm under Napoleon's leadership to its exploited state under Jones's rule is through Squealer. The minister of propaganda for the pigs is entirely committed to concealing the truth from the animals. When the animals begin any type of questioning, Squealer is able to manipulate the animals into believing that the pigs have the animals' interests at heart when it is evident that they do not. Squealer is one way in which Orwell is able to draw parallels between the farm under the rule of Jones and the condition under the pigs' leadership.
Another way Orwell is able to show how things exist under Napoleon's leadership is in the edicts that are passed. Only the pigs receive education and possess the ability to read or write. This keeps the other animals in a type of check and control under the rule of the pigs, similar to how Jones silenced their voice. The leadership structure is not democratic in terms of the other animals possessing power, as the pigs wield all the power and make all the decisions. Jones followed the same methodology in how he exerted all of the power. Finally, I think that the way in which Napoleon is shown to deal with dissent is akin to Jones. Both leaders used cruelty and physical repression to silence animals who complained about the way things were. It is in these aspects where Orwell is able to show how the farm under Napoleon's leadership is similar to the exploited state it existed under Jones's rule.