While I do agree about the difference in magnitude, while Nynaeve refused to give a promise she had no intention of keeping, she also wasn't put in a position where if she didn't give the promise, she wouldn't have got what she deemed necessary, whereas for Egwene if she didn't make the promises to the Wise Ones, she wouldn't have been able to learn more about the world of dreams.
While it is fair to say she should have accepted that, and decided not to find out more, once she decided she did want to find out more, there was only one way to get that information.
The lie regarding Aes Sedai began as trying to shore up Rand and Moiraine's authority, with Elayne and Nynaeve also pretending to be Aes Sedai, which then got to the point she didn't feel comfortable telling the truth given how much time had passed with the lie. However, she did admit to it in the end, though see below with my views on the price she pays.

Not sure I entirely agree, it is potentially losing the moral high ground, but that is only internally, much of the dishonesty / potential dishonesty for Nynaeve wouldn't have been found out by the people she was dishonest to, it was only her affected, and her feeling she would lose moral high ground, and so not be able to deal with others as effectively.
With Egwene, the issue more is that she seemed to follow the Aiel Wise Ones in her actions / thinking. The Wise Ones are the first group of people advising / aiding her that I think started strengthening her flaws.
Their views tended to be do what was necessary, and pay the price for it. However, with Aiel, the way of paying the price was always physical, and even if made Gai'shan, there never seemed to be any remorse on the Aiel side, if anything sometimes it was almost pride to take the punishment earned.
Egwene followed this, always happy to take the physical punishment earned, but never really showing remorse.

While her misbehaviour / current reality may be deplorable, if we accept that the reasons / origins are plausible and solid, and nothing has been done to show Egwene the error of her ways, why would we expect her to change?
The issue more is those around her encouraging her to keep going for more power.
Siuan is a good example of this, and in many ways I think Siuan has similar flaws to Egwene, the lie about the Red Ajah aiding Logain, to ensure the Salidar Aes Sedai continued to rebel because Siuan couldn't stand the lawfully elected Elaida remaining in charge being a good case in point.
The fact that Siuan thought that Egwene would make a great Amrylin, and told Egwene so, also reflects that she only encouraged Egwene's behaviour.
The other Aes Sedai tended to take a similar view, or tried to manipulate her so obviously, they couldn't help but ensure she carried on trying to strengthen her power and remove their manipulation.
In many respects, I think Egwene embodied the majority of Aes Sedai at that point, just didn't have the experience / age to be able to hide / soften it more, and is reflective of why I think the Aes Sedai as a whole were a pretty deplorable lot by the time of the Eye of the World.