Both are organizations that can do a lot of harm, but the Aes Sedai have more checks and balances on their power than do the Whitecloaks.

Tell me if you can. what mistakes did Shein Chunla make that caused the Third War of Garen's Wall? What were the causes of the Great Winter War between Andor and Cairhien? What caused the Weikin Rebellion and how did it end? Most of history seems to be the study of wars, and the important parts of that are how and why they began and how and why ended. A great many wars would never have taken place if people had paid attention to the mistakes others had made. [that's why Aes Sedai checks & balances keeps them SECRET! LOL] Well?"
"Shein didn't make any mistakes," Egwene said slowly, "but you're right. I do have a lot to learn. I don't even know the names of those other wars." Rising, she poured herself a cup of tea from the silver pitcher on the side table. Aside from the ropework silver tray, the tabletop held a stuffed lynx and the skull of a serpent. That was as big as a man's skull!
Bennae frowned, but not for the tea. She hardly seemed to notice that. "What do you mean Shein didn't make any mistakes, child?
Why, she bungled the situation as badly as ever I've heard of."
"Well before the Third War of Garen's Wall," Egwene said, returning to her chair, "Shein was doing exactly as the Hall told her and nothing they didn't." She might be lacking in other areas of history, but Siuan had tutored her thoroughly in the mistakes made by other Amyrlins. And this particular question gave her an opening. Sitting down normally took a great effort.
"What are you talking about?"
"She tried running the Tower with an iron hand, never a compromise on anything, running roughshod over any opposition. The Hall grew tired of it, but they couldn't settle on a replacement, so rather than deposing her, they did worse. They left her in place and forced a penance on her whenever she tried to issue an order of any kind. Any kind at all." She knew she was going on, sounding as if she were the one giving a lecture, but she had to get it all out. Not easing herself on the hard wood of the chair seat was difficult. Welcome the pain. "The Hall ran Shein and the Tower. But they mishandled a great deal themselves, largely because each Ajah had its own goals and there was no hand to shape them into a goal for the Tower. Shein's reign was marked by wars all over the map. Eventually, the sisters themselves got tired of the Hall's bungling. [They got "tired"? War everywhere? Checks and Balances! Petty, self-centered, bickering bitches is what they are] In one of the six mutinies in Tower history. Shein and the Hall were pulled down. I know she supposedly died in the Tower of natural causes, but, in fact, she was smothered in her bed in exile fifty-one years later after the discovery of a plot to put her back on the Amyrlin Seat." [Mutiny, murder, wars...all kept under the hat!]
"Mutinies?" Bennae said incredulously. "Six of them? Exiled and smothered?"
"It's all recorded in the secret histories, in the Thirteenth Depository. Though I suppose I shouldn't have told you that." Egwene took a sip of tea and grimaced. It was all but rancid. No wonder Bennae had not touched hers.
"Secret histories? A thirteenth Depository? If such a thing existed, and I think I would know, why should you not have told me?" [GOOD QUESTION! Because the Aes Sedai system is so good and fair I guess!]