Moiraine and Cadsuane both served the same role in that they both tended to keep Rand on an even keel, or as much as is possible but Moiraine was more the teacher who showed him the world, the game of houses and set him on the part of what he needed to do. Cadsuane is as near to an equal as Rand can get and is someone who can challenge him when it comes to strategy and tactics.

Before she arrived Rand was surrounded for the most part by yes men, even those who were loyal like Dobraine. Mat & Perrin had been sent off to do their own missions and Egwene, Nynaeve and Elaine were likwise engaged in their own projects. Min is too much in love with Rand to truely stand up to him.

When a leader has no one to challenge their ideas they can go astray and think that just because they think an idea is a good one it must be so. Moiraine could not perform this role, she could guide him, suggest things but not outright make him prove that his plan was the right one. She was too much of a known commodity as far as Rand went.

Likewise Cadsuane was the first Aes Sedai to open the door to Aes Sedai and Asha'man working together. She suggested that the three Asha'man with Rand be bonded and that idea seems to be taking off.

Lastly Cadsuane may not be terribly likable but I don't think she thinks that she is always right and in control. She had learned the lesson that its when things get hariest and the brown stuff has hit the fan that is the time you have to appear most in control, calm, not crumble. From her onw point of view she is certain she needs to reconnect Rand with his humanity but by no means is she certain she will succeed and this is her biggest fear.

When Rand turned on her, her fear was more about thinking she has lost her chance to help put Rand on the straight and narrow that that she was going to die. At least that was my read of the situation.