It is notable that many of Hobbes's references to Aristotle in Leviathan are very general:
I believe that scarce any thing can be more absurdly said in natural Philosophy, than that which now is called Aristotle's Metaphysiques, nor more repugnant to Government, than much of that he hath said in his Politiques; nor more ignorantly, than a great part of his Ethiques.
This is mere abuse. Hobbes does not specify what it is that Aristotle says to which he takes such exception. When he does address specific ideas, it seems that the abyss between Aristotle and Hobbes is not as wide and deep as it appears from his general denunciations. Hobbes agrees with Aristotle that we refer to the things we want as "good." He makes this point in terms that echo those of the Nicomachean Ethics, saying that "justice, gratitude, modesty, equity, mercy, and the rest of the laws of nature, are good; that is to say, moral virtues; and their contrary vices, evil."
Where Hobbes differs from Aristotle is in believing that these laws suggest the existence of a single ultimate good. Hobbes says that there is no possibility of such a thing. The achievement of the ultimate good would be the end of desire, and the desires of men never end:
Felicity is a continual progress of the desire, from one object to another; the attaining of the former, being still but the way to the later.
Hobbes therefore disagrees with Aristotle about both goodness and happiness, believing that both can only ever be relative and contingent. All our desires, including those for the things we think are good, cause conflict with others. The answer is not to seek some abstract idea of the good which will lead to happiness, but to have our brutish, egotistical natures curbed by an overwhelming external force: the Leviathan. Hobbes's alternative may be less appealing than Aristotle's idealism, but it is also more pragmatic and plausible.