I have heard that Mikimoto sources most of the very best akoya pearls from many farms, but don't know if that is true.
I do know there are pearls out there that do not belong to Mikimoto that are top quality, so they don't get
all of the best pearls by any means.
I also believe that one can buy a necklace that would be top quality on the Miki scale from a number of other akoya dealers. Though the competition is fierce and such fine necklaces are the most rare, it will still cost considerably less than a Mikimoto. The extra cost is for the brand and the clasp with the brand marked on it.
I have seen brand name Mikis that are not very good pearls compared to what one can get by spending the same money elsewhere.
We do have people here who should be able to answer your question more accurately although pearl grading is always on a continuum. Pearls always range in quality from the bottom to the top of the particular grade, whatever the grade is called.
Contrary to popular opinion, there is no standard grading for pearls, thus an Ebay AAAA pearl could be the equivalent of someones else's grade A or worse. Among the people who do not go to four A's, there is still variation. One outfit's AAA may be another's AA+. That means any one comparison you get would be only that person's opinion and could vary between legitimate sellers. Also, although it is not listed as a higher grade than AAA, the best of the AAA continuum usually gets a name, like elite pearls or gem quality pearls, to differentiate it from the rest of the AAA grade pearls.
I know I talked all around your question, but I always like to be able to take the opportunity to explain how much the brand name adds to the cost of the pearls.
There is one dealer in Japan who has been discussed on this website, but is not a member who has some mighty fine pearls and he also seems very knowledgeable about his pearls and Miki grades. The info is on his webpage. Without looking it up, I am fairly sure his name is Sakura Pearls. I actually don't like some of his definitions and opinions, but there is no arguing he has fantastic pearls. Anyway, an email to him could answer your question in addition to any other answer someone here may give you.
I just found Sakura's pages:
http://www.sakura-pearl.com/en/pearl/ but I saw no mention of the comparisan grading. In fact most of the other info I did not like is gone as well, except for that pesky "like a grain of sand" fable on the page I linked to here. It is impossible for a grain of sand to be covered with pearl nacre and become a pearl; oysters are made to be able to expel sand and suchlike from its shell by secreting mucus around the offending object and expelling it. Click on the link below my name to see the process in action.
In any case, that link will not answer your question, any more, so hopefully someone else will come along. But for anyone who read this far, he does have some stunning chokers with one pearl in the center and tiny gemstones for the rest of the necklace. drool.