I think the problem was not that Gawyn wasn't used to living in someone's shadow, it's that he wasn't happy about it. He always had hope for the future, that it would lead to glories that would allow him to step out from the shadows of his sister and brother, or whomever else. Instead, he gets exiled to a small town outside Tar Valon working for no good reason for people he hates while other people, especially the guy his sister likes that he thinks killed his mother, go about getting glory. This is what had made him so insufferable and twisted for so long, and it's something he didn't even recognize in himself.

But as a good match for Egwene, he's not some super-powered King of the world, and he's certainly not a hero with accomplishments anywhere near any of the main characters, but he's the second-highest ranking noble in Andor, a man trained to be a general, and possibly the best hand to hand fighter in the world. He's made out to be a smart thinker and a good strategist, and now that he's over his own personal issues, he's bound to be a good match for her. Not to mention that they love each other, so that's got to help things out some, too.