We know that the Aes Sedai of modern days set their rankings by the power. We don't know if this is so for the Shadow. When Mesaana appears in disguise to Alviarin, she hides her strength. That could be a general part of the disguise, though. Anyway, given how the Shadow operates, I suspect aptitude at completing assignments, surviving intrigue, and raw personal power are all factors. Remember that the case for the Foresaken being extremely strong to a random Randlander works like this: In the Age of Legends, channelers had unspeakable power. Some of them went over to the Shadow. The strongest of these (who survived, and happened to be having a Coffee Hour at Shayol Ghul when Lews Thern and his gentleman callers arrived and thus got bound in the dungeon dimension) are the Foresaken. While certainly strong, a Foresaken need not necessarily be earth-shatteringly strong. Moghedien appears to be an even match for an untrained Nynaeve and she's one of the strongest the Aes Sedai have seen in a thousand years. The Moggy isn't marked up as being exceptionally powerful among the Foresaken except for in the World of Dreams.
All of that said, the modern AS do rank by strength. Alviarin managed to become Keeper to Elaida. Some of that is surely intrigue strength and political interest, but she's no certianly no slouch in modern terms of Power either. She has enough juice to Travel. Of course, fair point that she's not the force she once was. But Shaidar Haran is impressed enough with her.