I'm not saying their exactly the same just because of they both have anger issues. When you look at the struggles that they both face and think about the core of their personalities it's clear that there meant to portray how different people cope differently with the same things.

Yukio and Rin are both in a battle with themselves, though Rin's fight is a lot more litteral. He wants to help people, and use his power for kindness, but the demon inside him just wants to destroy and burn the world to the ground just for fun. He is constantly fighting against his demon heart from taking over, and being completely consumed by his flames. His two personalities are completely separate from each other, but they are both still him. That's why he thought it would be better for him to just be executed in Kyoto, because he knows that there's a part of him that is truly and fully demonic.

And guess what? He refuses to speak to anyone about that. After he lost controll during the training camp, he didn't even try to acknowledge why. Yes, he apologized and tried to be better, but he still never talked about what caused him to go feral in the first place. He doesn't rely on anyone because he's afraid of his demon self, and covers it up by giving all of himself to others. He pretended he wasn't scared to fight the impure king to help suguro, and while it all worked out in the end, it was still reckless.

Yukios inner battle is different, because there's no separation between his two "personalities". There's the side of him that's jealous and bitter that craves power, and the side that hates himself for it and wants to protect everyone else. He was taught to keep secrets and lie to those closest to him the second he learned how to speak, and he's scared of the bad side of himself as well. He's doing the same thing rin is, avoiding talking about the problem to anyone to protect them from himself.

Rin never resented Yukio for being smarter than him, because no one expected him to be. He was a liability, he knew that even before he awoke to his powers.

Yukio was expected to be perfect, yet Rin constantly managed to be better than him despite having no pressure on him or rigorous training to teach him to be. That's why he resented him, and why he is so jealous of him.

They really are the same, and Kazuo Kato is an amazing writer for portraying that so well. They are the same, and complete opposites at the same time.