I'm not an expert, but this is what I've gathered from hanging around on the pearl boards for awhile. First, "Mikimoto" and "Pearl Paradise" are both the names of companies, so your question is probably too broad to answer with much accuracy. I hear Mikimoto is very overpriced, as you are paying an extreme premium for the name. Some people do want that brand and the trademark clasp to prove it, so I guess that's fine as long as they realize that they are paying much more for the brand name.
What I think of when I hear "Mikimoto" is akoya pearls (although they now sell other types). Pearl Paradise has those, and freshwater, and etcetera. All I would think could be said from your question is that both PP's AAA and Mikimoto are high quality. Beyond that, we would have to compare like items from each company to assess which is "better." Hope that helps.
Is there an agency that decides which pearls are graded AAA? or does the vendor designate the grade? (For example, GIA is an independent lab that grades diamonds. Is there an organization that does that type of cert so that pearls get A, AA or AAA grading?)
It really boils down to this: Are PPs AAA pearls the same quality as Mikimoto's AAA akoya pearls (without paying for the name, of course)?
There are no universal grading scales for pearls. I would think that Pearl Paradise is as stringent as Mikimoto in grading their pearls. If you look at both they tell you what to expect with each grade you select. I have not purchased from Mikimoto but I have many times from Pearl Paradise. I like that there are NO surprises and get just what I was hoping for when I buy there. http://www.pearlparadise.com/Akoya-pearl-grading.htm http://www.pearlparadise.com/Freshwater-pearl-grading.htm