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In Mill's Utilitarianism, he attempts to layout groundwork which removed subjectivity from the good in a thing. When I read this, it just seems like he's naysaying his relationship to the virtues laid out by Aristotle.
Why does Mill think his view does not work out to just being an application of Aristotle's virtue?
There's two things at work here that I think help explain how Mill is not merely providing an expression of Aristotle. (You can also look at "pleasure" vs "happiness" and What is the causal connection between virtues and eudaimonea in virtue ethics? )
For one thing, it's not clear that Aristotle and Mill agree about the nature of happiness. One hint is that Mill seems to identify happiness with pleasure. For Aristotle, pain and pleasure signal right and wrong but only for the phronemos (man with practical wisdom) (NE Book 2). What Aristotle means by "happiness" is eudaimonia, a concept that invokes both "happiness" and "flourishing" and other things at the same time. In other words, it should not be identified with pain and pleasure.
At the same time, Mill does distinguish between two types of pleasure in Utilitarianism. One type of pleasure is "base" and the other "noble". But at least in my view, there's little argumentation in support of this claim in Mill's account. (Looking at it historically, this is an evolution to fix a problem with Jeremy Bentham's utilitarianism where pleasure/pain are not differentiated at all -- so everyone getting drunk every night may be the best way to maximize happiness for the most people).
The second issue is that Mill is committed to a calculative approach to morality, "the moral calculus." In contrast, Aristotle is committed to a reasoned approach to morality. It seems doubtful he thinks it can be calculated (even if it involves moderations between extremes and "fit" to one's own nature).
To reword the second claim I'm making, Aristotle is committed in part to saying regular people cannot simply calculate morality. Instead, what is right is somewhat opaque to them because they act from confused signals and poor upbringing. To know what to do rightly requires being a phronemos. For Mill, right courses of action are apparent because we just need to calculate what will bring about the most pleasure (of the right kind), which he doesn't propose to be a daunting task available only to a few.
These two considerations aside, Mill might say he's just perfecting Aristotle. After all, his claim regarding Jesus is that if/since Jesus is doing good, Jesus is maximizing pleasure for the most number (I think this is in Utilitarianism chapter 4 but I could be off on the chapter).
