I wanna say it's "One Of These Things Is Not Like The Others," but I don't think they really have enough in common that only one of them is different ...
... wait, I know! Satori's the only one who, when you beat her, doesn't end the current game-mode (outside of Practice, which EX-stages don't have)! ... um, and she's the only one who uses other peoples' attacks! And directly reads minds! And is someone's older sister! Um ...
I found that the height of them are in descending order... Satori is the shortest inside. And, the ranks of them are also in descending order: Nue(UFO extra boss), Koishi(SA extra boss), Flandre(EoSD extra boss), Utsuho(SA stage 6 boss), Satori(SA stage 4 boss) Extra stage>Stage 6>stage 4 UFO>SA>EoSD
You ALL are missing the point. They all have something that has something to do with an Eye.
Satori + Koishi - Third Eye Utsuho - The eye on her chest Flandre - Crushes the "eye" of something. Nue - Can disguise herself from the eye. (grasping at this one.)