I wonder if you might have misunderstood this question. Diamond does not argue that Mesoamerica had advantages. Quite the contrary, he discusses the advantages enjoyed by the Fertile Crescent at length in Chapter 5.
In Chapter 5, he lists five advantages that the Fertile Crescent enjoyed when it came to food production. He talks, for example, about how many species of domesticable plants and animals existed in the Fertile Crescent and about how the plants there were better than plants elsewhere. After he gets done listing all of the advantages that the Fertile Crescent had, he says, on page 142 in the paperback edition, "the situation in Mesoamerica contrasts strongly" and goes on to say that Mesoamerica lacked domesticable plants and animals.
Therefore, I believe that you must have misunderstood the question.
It's been a while since I've read the book but perhaps homer is refering to the efficiency of the Mesoamerican milpa system of agriculture.
I believe Mr. Diamond mentioned that if given the amount of lead time that the fertile cresent bundle of agricultural goods had, the Mesoamerican bundle of agricultural goods (the milpa) would have provided more nutrition and allowed for the establishment of equally if not more complex bureaucracies.