As for that, it depends quite a bit. Egwene's arrogance remains largely consistent throughout the series, while Rand's is perpetually growing. Eye of the World Rand is far less arrogant than Egwene, but Knife of Dreams/The Gathering Storm Rand is far more arrogant than her.
I think - as far as I am concerned anyway - that the difference is not so much in the arrogance of the characters themselves, but in the ones who surround them. Rand was perpetually hounded by people far more arrogant than he, so when he starts counter-arrogance, it's easy to side with him. Whereas Egwene was, in the early series, one of those more arrogant people.
More importantly, Rand is surrounded by people dedicated to keeping him humble, from Cadsuane to the likes of Egwene herself. So the desire to defend him pops up as a contrarian instinct. Meanwhile, Egwene was largely surrounded by people who kept praising her or were obviously wrong, so I just want to drop her down a notch.
I think that is fair, and I think shows that Egwene was never really getting the support she needed, and Elayne and Nynaeve disappearing almost as soon as they were reunited in Lord of Chaos didn't help that either.
In some respects it is somewhat ironic or amusing, though potentially poor writing, that the Aes Sedai, who invented the Daes Dae'mar, were really so poor at it when it came to trying to manipulate Egwene, compared to those who supposedly amateurs in comparison to Aes Sedai and their dealings with Rand.
I think in some ways it is fortunate for Egwene that she didn't survive the Last Battle, and in the aftermath have to start dealing with those who wouldn't praise her or be obviously in the wrong.
