Utilitarianism By The Scenic Route
One of the main themes of the book is to propose an alternative to utilitarian theories of animal "rights." But as far as I can tell, a bit of work with Occam's Razor would reduce his theory to utilitarianism at its core. Besides the strange equality-based objection I discussed in my previous post, Regan has two main issues with utilitarianism. First, he says that utilitarianism treats persons* as merely containers for welfare. So what's valuable is your welfare, not you yourself. Second, utilitarianism cannot justify a strict rule against harming others, since it's always possible that the factual circumstances will be such that harming another person would maximize utility.
Regan's alternative begins with a claimed denial of the container view. All persons, he says, have equal inherent value that is independent of how much welfare they contain. Our primary moral duty is to "respect" that inherent value. "Respecting" a person's inherent value prohibits treating them as solely a container for the welfare we seek to promote. Rather, "respecting" a person's inherent value consists in ... promoting their welfare. Stated in this blunt (albeit, so far as I can tell, accurate) fashion, Regan's postulation of inherent value has no practical effect. We get to the same result, but with an added rhetorical gambit that makes his theory sound nicer than his description of utilitarianism.
Turning to the question of strict rules against harming persons, Regan's theory also fails to make an improvement over utilitarianism. He (correctly) avoids trying to narrowly circumscribe what harms actually count as real harms in such a way as to eliminate the possibility of clashes between different persons' welfares. But in allowing situations in which a choice must be made between the welfares of persons, Regan's theory ends up once again as utilitarianism-by-the-scenic-route. A utilitarian says to the person who gets the short end of the stick "I'm reducing your welfare in order to make an improvement to the welfare of someone else." Whereas Regan says "I'm disrespecting your inherent value by reducing your welfare in order to respect the inherent value of someone else by making an improvement in their welfare." Once again, the concept of inherent value does no philosophical work (though it does a lot of rhetorical work), because respecting inherent value merely consists in promoting welfare.
Nevertheless, I do think the tendency of Regan's anti-container view to collapse into utilitarianism suggests the weakness of the "container" objection to utilitarianism. The container objection's plausibility rests on thinking of welfare as a substance (a la money) that exists independently of the container. But in fact welfare is a relational property, that is in part defined by the container. And for both Regan and utilitarians, what makes the container morally important is its ability to contain welfare. So respecting the welfare-holder and filling it with welfare are not really separate ideas.
This is not to say that Regan's theory is identical to utilitarianism -- they differ in two key respects, though these are not differences that allow his theory to evade the criticisms he makes of utilitarianism. One is their definition of welfare. Utilitarians of all stripes are united in adhering to a subjectivist account of welfare -- that is, what's good for a person is defined by that person's viewpoint, e.g. the preferences they express or the pleasure and pain they experience. But Regan proposes a partly objective view of welfare, in which it's possible to ask if what a person prefers or enjoys is in fact really in their interest (though it's unclear how one would go about finding an answer). The second big difference is the rule for dealing with conflicts among different persons' welfare. While, as noted above, Regan admits the necessity at times of sacrificing a person, he proposes to make such choices in accordance with a variety of priority rules rather than on the basis of a utilitarian maximization rule.
*I'm using "person" in the philosophical sense, by which both Regan and a utilitarian would count animals as persons.