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.
There's also the detail of Rand coming off as a overly stressed "kicked puppy" where as Egwene... Well, she sure comes off as a type of dog anyway.
It's a lot easier to feel forgiving of the slowly going mad guy tasked with saving the world and dieing, then it is the... Well, the best way I ever heard her personality described was "politician", and one who wouldn't know the meaning of the word "friend" if it was shoved up her ass... Which is made all the worse, as she naturally ends up being judged on such matters by the yardstick that is.. Near everybody else from the TR, most all of which would go to the Pit of Doom for a friend(two of which did just that).
Possibly, but at the same time, perhaps Egwene would have gone to the Pit of Doom if needed.
Both Rand and Egwene at times treated their friends harshly, when circumstances demanded it.
