Rand's scenario is this: He is the sole person who can save the world, and the absolute best he can hope for is to die in the process. He has the voice of a LTT, the Kinslayer, in his head, he channeled a tainted Saidin out of necessity for ages, he's had everything and everyone he loves taken from him, turned against him, or in the worst, been forced to act against those he loves (his actions towards the Two Rivers and especially Min). Oh, and he was stabbed by Fain's blade. We know how corrupting his voice is (look at Elaida) so imagine what that wound is doing? Not to mention Ishmael's wound.

Oh, and then there's fun little experiences like losing a hand to a fireball, being shown that your mother, who you never even met, is being personally held and tortured by the Dark One himself, being kept inside a box for a month and being let out only to be beaten (or worse - to helplessly watch your loved one being beaten)...

Honestly, it's a miracle that Rand didn't just destroy the world. He has flaws, true, but in his case the majority of his bad judgments can be attributed to the way life has shaped him.

Egwene on the flip side, has been pampered by the author. All of her bad judgments are excused or ignored because of the way the books are written (for example, why not keep at least SOME of the BA prisoner? Still them first to be safe, but don't miss out on the information they hold!). While I liked Egwene well enough in KoD, I think TGS played her into the martyr role a little to easily for me take it seriously. She hasn't actually experienced any mental hardships that I can think of beyond the physical treatment she received, and that pales against what Rand got.