I believe this is what was pointed out in the TidBITS article (although it seemed to dwell on GMail); if the mail boxes on the server are not the same as the mailboxes on you computer, one named as it is on the server may be created on your machine. For example, on the MacBook, there is a folder called "WPNA" with one subfolder. But on the iMac, it is a separate Folder with that hierarchy. I don't know which way it is 'seen' on whatever servers you have at the various ISPs (I see mindspring.com, englandphoto.com and, I assume, iCloud). When a message comes to one of those servers and it has a different folder arrangement than you have on either computer, it may cause a new folder to be created there. Which computer checks and downloads the message can mean that the folder will not appear on the other one. I'm grasping at straws and what I think I understood about that article, also.
Secondly, the hierarchy is just the same on the two machines, thus the items I mentioned above. More importantly may be the different spellings of at least two mailboxes; the "Teaching" folder is under two different main folders, there is a difference in the spelling of the sub-folder in that Teaching folder: "my notes" is not the same as "My notes".
I would suggest first arranging all the folders in the same order on both computers, I think it would just make it easier to find things.
Naturally, it would help to see differences in spellings as well as missing folders/mailboxes. Then, compare the rules in both computers. Unfortunately, I don't know of a way to print those out or export as text files that could then be compared digitally. If you do have an iCloud account, you can upload/store your rules there (iCloud Documents & Data) and at least have the same ones be applied with both computers. As an aside, I might select a font or font size that allowed the displaying of descenders of the folder/mailbox labels; right now the descender of a "y" is cut off and sure looks like a "v"!
Or just use only uppercase characters? Or just ignore my whining!
Frankly, I just don't think Apple planned on having more than one computer connected for each person. "Multiple devices" seems to mean
A computer and
An iPad and/or
An iPhone, but not
two of anything!
And I often see a message on my iPad or iPhone that shows up as UNread, but I have already read on my iMac. This may also have something to do with how I have Syncing set up, however.