I've been re-reading a lot of Mill lately, and one thing that jumped out of me this time was that a major element of Mill's rejection of Bentham is that he doesn't think Benthamite utilitarianism can function as an ethics. This is a repeated criticism in the essay on Bentham. I thought it might be interesting to collate some of the passages in which he points this out.
(1) Man is never recognized by him as a being capable of pursuing spiritual perfection as an end; of desiring, for its own sake, the conformity of his own character to his standard of excellence, without hope of good or fear of evil from other source than his own inward consciousness. Even in the more limited form of conscience, this great fact in human nature escapes him. Nothing is more curious than the absence of recognition in any of his writings of the existence of conscience, as a thing distinct from philanthropy, from affection for God or man, and from self-interest in this world or in the next. There is a studied abstinence from any of the phrases which, in the mouths of others, import the acknowledgment of such a fact. If we find the words ``conscience'', ``principle'', ``moral rectitude'', ``moral duty'', in his ``Table of the Springs of Action'', it is among the synonymes of the ``love of reputation''; with an intimation as to the two former phrases, that they are also sometimes synonymous with the religious motive, or the motive of sympathy. The feeling of moral approbation or disapprobation properly so called, either towards ourselves or our fellow-creatures, he seems unaware of the existence of; and neither the word self-respect, nor the idea to which that word is appropriated, occurs even once, so far as our recollection serves us, in his whole writings.
(2) Morality consists of two parts. One of these is self-education; the training, by the human being himself, of his affections and will. That department is a blank in Bentham's system. The other and co-equal part, the regulation of his outward actions, must be altogether halting and imperfect without the first; for how can we judge in what manner many an action will affect even the worldly interests of ourselves or others, unless we take in, as part of the question, its influence on the regulation of our or their affections and desires? A moralist on Bentham's principles may get as far as this, that he ought not to slay, burn, or steal; but what will be his qualifications for regulating the nicer shades of human behaviour, or for laying down even the greater moralities as to those facts in human life which tend to influence the depths of the character quite independently of any influence on worldly circumstances,---such, for instance, as the sexual relations, or those of family in general, or any other social and sympathetic connexions of an intimate kind? The moralities of these questions depend essentially on considerations which Bentham never so much as took into the account; and when he happened to be in the right, it was always, and necessarily, on wrong or insufficient grounds.
(3) That which alone causes any material interests to exist, which alone enables any body of human beings to exist as a society, is national character: that it is, which causes one nation to succeed in what it attempts, another to fail; one nation to understand and aspire to elevated things, another to grovel in mean ones; which makes the greatness of one nation lasting, and dooms another to early and rapid decay. The true teacher of the fitting social arrangements for England, France, or America, is the one who can point out how the English, French or American character can be improved, and how it has been made what it is. A philosophy of laws and institutions, not founded on a philosophy of national character, is an absurdity. But what could Bentham's opinion be worth on national character? How could he, whose mind contained so few and so poor types of individual character, rise to that higher generalization? All he can do is but to indicate means by which, in any given state of the national mind, the material interests of society can be protected; saving the question, of which others must judge, whether the use of those means would have, on the national character, any injurious influence.
(4) In so far as Bentham's adoption of the principle of utility induced him to fix his attention upon the consequences of actions as the consideration determining their morality, so far he was indisputably in the right path: though to go far in it without wandering, there was needed a greater knowledge of the formation of character, and of the consequences of actions upon the agent's own frame of mind, than Bentham possessed. His want of power to estimate this class of consequences, together with his want of the degree of modest deference which, from those who have not competent experience of their own, is due to the experience of others on that part of the subject, greatly limit the value of his speculations on questions of practical ethics.
(5) He is chargeable also with another error, which it would be improper to pass over, because nothing has tended more to place him in opposition to the common feelings of mankind, and to give to his philosophy that cold, mechanical and ungenial air which characterizes the popular idea of a Benthamite. This error, or rather one-sidedness, belongs to him not as a utilitarian, but as a moralist by profession, and in common with almost all professed moralists, whether religious or philosophical: it is that of treating the moral view of actions and characters, which is unquestionably the first and most important mode of looking at them, as if it were the sole one: whereas it is only one of three, by all of which our sentiments towards the human being may be, ought to be, and without entirely crushing our own nature cannot but be, materially influenced. Every human action has three aspects,---its moral aspect, or that of its right and wrong. its aesthetic aspect, or that of its beauty; its sympathetic aspect, or that of its lovableness. The first addresses itself to our reason and conscience; the second to our imagination; the third to our human fellow-feeling. According to the first, we approve or disapprove; according to the second, we admire, or despise; according to the third, we love, pity or dislike. The morality of an action depends on its foreseeable consequences; its beauty, and its lovableness, or the reverse, depend on the qualities which it is evidence of. Thus, a lie is wrong, because its effect is to mislead, and because it tends to destroy the confidence of man in man; it is also mean, because it is cowardly; because it proceeds from not daring to face the consequences of telling the truth; or, at best, is evidence of want of that power to compass our ends by straightforward means, which is conceived as properly belonging to every person not deficient in energy or in understanding. The action of Brutus in sentencing his sons was right, because it was executing a law essential to the freedom of his country, against persons of whose guilt there was no doubt; it was admirable, because it evinced a rare degree of patriotism, courage and self-control: but there was nothing loveable in it; it affords either no presumption in regard to loveable qualities, or a presumption of their deficiency.
Some brief comments.
(1) We get some notion of the shape of ethics as Mill sees it: it accepts the existence of conscience, moral aspiration, self-respect, and duty as facts of human nature, and reasons accordingly.
(2) Self-education, as one might expect, plays an extremely important role in Mill; and, indeed, the whole of Mill's deviation from Bentham is arguably summed up in the second passage above: he regards it as essential to moral theory. If your moral theory says nothing about self-education, about cultivation of character, about training of will, it is not moral in the strictest sense at all, but something else; it is missing what is required for handling morality as such.
(3) I find the 'national character' bit interesting. This used to be quite the common concept. Whewell, Mill's rival in moral philosophy, talks about it; Hume has an essay on it in which he tries to pin down the best way to account for it. But it tends to be out of favor today, largely, I think, because it has always been used in an ambiguous way, as part descriptive and part normative. If I say 'candour', i.e., honest forthrightness, is part of the British national character, this needn't mean that I am saying that all of the British are candid, nor even that the majority are; rather, it probably means that candour is (so to speak) part of the goal of being British. It's a public standard, a shared value, a continual task being British gets you. But I could also use the phrase descriptively, and say, the British national character has deteriorated from the days when candour was the national virtue. Here, clearly, we are making a descriptive claim rather than a normative claim. But Mill gives what can be seen as a sort of account for the duality of the term: namely, the national character is a generalization of individual moral characters (it is unclear whether it is a generalization from all the individual characters, which seems unlikely, or, much more probably, a generalization from the characters of prominent individuals); a sort of moral fact about a society that emerges from considering the moral character of the people in it. Thus Mill's use is purely descriptive, in the way I would say, "Each person should work on what will improve their character."
(4) The three-aspect thesis is striking; and, ultimately, what it amounts to is that Mill recognizes that in addition to the standard moral ideas (obligation, etc.), it is necessary to have room for the cultivation of moral taste.