The first contrast Rawls draws in the sixth section is between the two theories' response to common sense morality. Again, as was pointed out in the previous posting, Rawls has Sidgwick implicitly in mind here given that the Methods of Ethics took seriously from the first the notion of "common sense morality". Naturally Rawls' response to the challenge of common sense morality differs from that of Sidgwick since Rawls assumes that justice as fairness can take the claims of common sense morality more seriously than can utilitarianism. The main reason given for taking this to be true is that the convictions of common sense morality concerning justice are assumed to be consequences of the principles that would be chosen in the original position. This assumption is quite different from the utilitarian one which adopts the more empiricist argument of viewing common sense morality as having a generic good function even though the rules of it are secondary to those of utilitarianism. (Rawls does not here invoke the general "Government House" conception that Sidgwick adheres to of taking the dictates of common sense morality to be ones that might be publicly adhered to whilst secretly one is committed to utilitarianism. Given Rawls' own conviction of the importance of the publicity of principles of justice and the way this conception cuts directly against requirements of common sense morality we have here a stronger argument for viewing justice as fairness as taking common sense morality more seriously than utilitarianism than Rawls gives in the text!)
The second contrast between justice as fairness and utilitarianism is the more familiar one that suggests the contractarian nature of the former is effectively more social in form than the principle of the latter given that the latter extends the principle of choice for one man to the whole of society. This contrast invokes the charge of abstraction from the separateness of persons against utilitarianism and so is simply a restatement of the argument of the fifth section.
The third contrast invokes the distinction between deontological and teleological approaches to ethics, a contrast related to the question of the priority of the right over the good or vice versa. The sense in which justice as fairness is a deontological view is specified here as being that it does not interpret the right as maximising the good. Whilst this point is familiar in some respects the means by which Rawls defends it in this sixth section is unexpected. It concerns the manner in which the good is taken to be prior to the right by utilitarians. If the utilitarian theory is viewed as giving priority to the good over the right the natural question arises concerning what the good is taken to be by this theory. Here Rawls makes the key point that the good is simply assumed to be that which is desired. In other terms, whatever is desired would appear to have value so the question of maximisation arises due to a prior commitment to this conflation of the good with the desirable. It is natural to wish to maximise the desirable and if the good is viewed through the prism of the desirable then the maximisation strategy is intuitively plausible as a whole.
However, following Kant's argument concerning the nature of happiness, Rawls does not accept a prima facie value as attached to whatever is desired. Rather, Rawls takes it to be the case that only that which matches the principles of right has value. The principle of right restricts (and thereby realises) what can be taken to be good. This is the point of the notion of the priority of the right over the good: the right provides us with formal characteristics that have to be satisfied in order that something can be taken to be good. In lieu of these being satisfied you merely have something that some may wish for but not something that has any status of value as such. As Rawls puts this: "desires and aspirations are restricted from the outset by the principles of justice which specify the boundaries that men's systems of ends must respect". So only certain kinds of ends will be taken seriously as only these ends are worthy of being taken seriously (just as Kant writes that it is only under certain conditions that one is "worthy of" happiness).
Because of the way the contrast between utilitarianism and justice as fairness has here been characterised the priority of the right over the good becomes clarified as central to the conception of justice that justice as fairness elaborates. It has a moral ideal that guides the selection of any possible end as being acceptable as a value and there is therefore no value in a basic sense prior to the formal criteria of right. This second set of contrasts hence makes much clearer the core conceptions of justice as fairness.