The potential advantages of global consequentialism are many. The addition of new focal points increases the expressivity of consequentialism. It allows consequentialists to directly answer questions about the best motives, the best system of government, or the best way to decide what to do. This also allows consequentialists to bring consequentialism into the strongholds of deontologists and virtue ethicists: it provides an explanation of the importance of character and of rules of conduct, going so far as to show how many acclaimed virtues and rules have systematically led to good consequences, and even daring to suggest ways in which they might be improved.
The striking thing about this passage, to my eye, is that none of the benefits mentioned are distinctive to global consequentialism (GC). They're all benefits of having an axiology, which every consequentialist has. (It's not as though anybody else lacks the theoretical resources to "show how many acclaimed virtues and rules have systematically led to good consequences". Given an axiology, such evaluation comes along for free.)
So we may ask whether GC adds anything beyond the kinds of evaluations that are already open to any consequentialist. Compare: the distinctive addition of Act Consequentialism (AC) is to further claim that the best act is also right, i.e. what we have most reason to do. Some global consequentialists might think that we can similarly make substantive new claims by applying these deontic or "normative" terms to everything, not just actions. Ord calls this view "normative global consequentialism". Others (e.g. Kagan, Parfit) only use the term 'right' in relation to acts, and restrict themselves to evaluative terms (like 'best') when assessing other kinds of things, like climates. Ord calls this view 'semi-normative global consequentialism'.
As far as I can tell, 'semi-normative global consequentialism' is just another name for act consequentialism. It does not even appear to make any different claims. Normative GC appears to make different claims, but this appearance is (I argue) deceiving. My argument for this was given in my post, 'Reasons Deflate Global Consequentialism'. There I suggested that, in calling a disposition (or climate, or other arbitrary evaluand) 'right', there is nothing else that the global consequentialist could plausibly mean, except that it is the best (of those available). So they are not really making a new claim. They are making an old claim, simply using new words.
The case of actions is importantly disanalogous. There are reasons for action, in addition to reasons for desiring that some action be performed. Evaluations concern what is good or desirable, i.e. what we have reason to desire. But beyond evaluating whether we have reason to want that an action be performed, there is a further question to address: whether the agent has reason to act so. The question whether an act is 'right' may thus be taken to address this second substantive question.
There is no such second substantive question when considering arbitrary other evaluands, like the climate. We have reasons to desire that the climate be temperate, say. But the climate does not have reasons to be temperate. Climates are not subject to reasons in this way. That is why there is no substantive question whether a climate is 'right', over and above the evaluative question whether it is best (of those available).
(Motives are, like acts, susceptible to two substantive questions. Aside from the question whether a desire that P is desirable, we can also ask the first-order question whether P is desirable, and hence whether we have reason to desire that P. Similarly with beliefs, we can ask whether we have reason to believe that P, independently of the question whether such a belief-state is desirable. But global consequentialism does not address these substantive questions -- or, if it does then it gives incorrect answers! Not every fortunate belief or desire is reasonable.)
Let's close by considering Ord's argument that [normative] GC is a distinct view from AC:
[I]t is logically consistent to claim that Michael should follow decision procedure Y even though his following decision procedure X would lead to a better outcome. This is closely analogous to the way that deontologists and rule-consequentialists can consistently claim that Michael should do act Y even though his doing act X would lead to a better outcome.[*] Act-consequentialists must be consequentialists about acts, but nothing in the letter of the view stops them being nonconsequentialists about decision procedures.
As my above remarks suggest, this analogy won't work unless one thinks that decision-procedures are, like actions, subject to an autonomous class of reasons. (And it certainly won't carry across to things like climates.) There is room for substantive dispute about whether our reasons for action derive from considerations of desirability (i.e. evaluative facts). This is how we can make sense of being a (non)consequentialist about acts. It's far less clear how to make sense of (non)consequentialism about climates or decision procedures. There does not appear to be logical space for such a dispute. There is no open question here to invite such competing answers.
Ord claims that there is an open question - 'should Michael follow decision procedure Y?' - that is not analytically settled by the evaluative fact that it would be better that Michael follow decision procedure X. I have no idea what he has in mind.
For example, one might be asking whether it would be rational (fitting) for Michael to use decision procedure Y. But then the global consequentialist gives an incorrect answer to the question: the most fortunate decision procedure is not necessarily the most rational. So that cannot be the sense of 'should' that Ord has in mind.
More generally, I think, when we ask the global consequentialist, "Exactly what are you claiming here?", they will either answer with a merely evaluative fact (hence already contained within any consequentialist's axiology), or else they will say something false. If they think they can say something both new and true, I have yet to hear what it is.