If the shells are thinner, they should be easier to peel. I have found that if you put plenty of salt in the water, they are less likely to crack. I have even seen slightly cracked eggs in the boiling water, but couldn't find any cracks when I went to peel them.Isn't Google evil fun? Can be a great time-waster, but fun. Anywho, re: eggs. I've never heard that "A" eggs have thinner shells but I'll have to make a point of seeing what grade goes into the water next time I do them. What I do remember reading in the difference between A and AA is that the yolks on the AA "stand up" nicer so you should use those if you want to make prettier sunny-side up ones.
I'm guessing CW will come strolling through here again soon, correcting our misconceptions and "cluck-cluck"ing her tongue at us like she does Myrtle and Company. Not complaining CW - you know we all appreciate your help!
The yolks on fresher eggs stand up taller. The ratio between height and diameter is one of the ways used to calculate the freshness of eggs.