Cadsuane knows that the WO greatly respect Egwene, and who knows what "proud mama" Sorilea has said about her? Either way, the fact is that Cadsuane has heard only good things about her, from sources she respects more than most others she meets.

Plus, Egwene herself is not the type to get intimidated in any way. Legendary status notwithstanding, Egwene's going to have no problem with meekness around anyone. Remember, she's a legend herself. She wiped out the Blacks, took back the Tower, and was the only reason the whole Tower did not become a bunch of damane. One way or another, she's achieved enough that she's already getting genuine respect and fear from other AS, not unlike Cadsuane herself.

And a lot of this will reach Cadsuane's ears too. The end result is going to be that Cadsuane will probably treat Egwene as she did Amys, probably with more deference since she's Amyrlin.

I frankly doubt either will care to intimidate the other. Cadsaune is going to be glad that a genuinely tough woman is Amyrlin, and Egwene, given her recent irritation at the Aes Sedai, is going to be relieved there are still some who seem capable of thinking beyond themselves.

I wouldn't be surprised if Egwene tries to recruit Caddy for her "toughen the Aes Sedai for TG" plan. Maybe Cadsuane will be given the charge of ensuring the Aes Sedai and Asha'man work together and lose their distrust? She's certainly the only one I can think of who can achieve that little miracle.