I never heard of the rule that the MOB picks first. What's the reasoning? Doesn't seem fair to me. Seems like it's going along with the silly idea that the wedding is "the bride's day."
Traditionally speaking, she's the hostess. She's doing all the heavy lifting in terms of planning, etc. (Traditionally speaking, remember.)
And if the two high-profile women, who are going to be memorialized in photos, are going to both contrast and coordinate their outfits, so that one of them isn't in sequins and the other in a less glittery outfit, or one of them is in a hat and the other not, and then one of them feels overdressed or underdressed, which is uncomfortable--well, SOMEone has to go first.
And so the hostess does, because she also sets the tone for the party itself. How formal? There ARE shades of formality in women's dress.
By sharing info about her choice, she allows the other matriarch to choose clothing that is in a simlar vein, so she doesn't feel she's overdone it or underdone it.
She can also provide info to any family members on her side who are saying, "Are sequins too much?"
So, picking her dress first is not necessarily a prize; it might be a responsibility.
Just as the MOB's entrance is not actually a gesture of honor--she is the last to sit down due to her responsibilities as hostess. She's been working up to that point, and no good hostess sits down and takes her leisure until her guests are situated.