Taim is actually pretty simple. He's just an average powerful channeler who has avoided madness for a time. He ain't Demandred, etc. because he was captured by Aes Sedai and I can't imagine one of the Forsaken allowing himself to be shielded or risk stilling, no matter what the circumstances or plot. It's as simple as this. Taim begins to go insane and begins using the Asha'man recklessly -maybe killing Aes Sedai for no reason- and Logain steps in and kills him. Logain's stilling delayed the onset of his madness, and he has a sense of justice that Taim did not. Logain makes the Asha'man more palatable and cooperative and leads them to glory in the Last Battle, though he himself dies. Logain does manage to get back at the Red Ajah, too. Wait and see...