Hobbes' state of war is the basis for his philosophical discourse on human nature. Where Rousseau says that man is compassionate and good to others in his nature, Hobbes argues that man is only out for himself.
When the point comes where two men want the same thing, they become enemies of each other. Since men often want the same things, they will try to take whatever they can get from each other. Therefore, any man's possession is not safe as long as someone else wants it. From this comes the constant state of war of everyone wanting what another possesses. With no government instituted every man is against the other with no median in which to protect anyone. Because everyone is against the other in war, there is no right or wrong, or any basis for these. There is no justice or injustice because these come from laws, and there is no government.
Rousseau would then argue that men come to peace and work together instead of against each other because it is good for them, and wouldn't like to see another man hurt. Hobbes says that man comes to an agreement of peace purely on fear. Man realizes that each person has the ability to kill the other, and therefore wants to be protected; so they declare peace to not kill one another. Whereas Rousseau says that man comes to peace because each cares about the next, Hobbes says that it occurs because it is in the best interest of a person for personal gain.
The difference between Rousseau and Hobbes is the factor of sympathy. Rousseau would argue that man would help another man who was injured because he would feel bad and want to help him. Hobbes would say that the only reason a man would help another if he were to get a reward for the deed. If a man is hurt, then one could possibly become hurt in the same way if he helped him, so why should he?
In the same way, Rousseau would say that if a man's neighbor needed food, he would give it to him because he ...