It's called background. Kakashi, Obito, and Sasuke, all three of them, have different backgrounds.
Kakashi, with the death of his father, was no stranger to death on a personal level by the time he became a ninja. Additionally, and the most important part, he's not an Uchiha. He benefitted from the "death" of Rin and Obito both, by gaining the mangekyou sharingan and sharingan respectively. Additionally, he does still carry a burden, he isn't completely over it; he just handles it very much differently, as in the end, his upbringing and surroundings didn't hint towards the great revenge path. Who would Kakashi have to go vengence commando on anyways? Himself and some already dead Mist ANBU?
Obito, the black sheep of the Uchiha back in his early days, liked to help old people, and based on his demeanor and reaction to Rin's death, he was not too familiar with the effects of death. Nevertheless. he saved Kakashi and gave him his sharingan, hoping that he'd use it to protect Rin. When Obito realized he still lived, he dreamed of reuniting with Kakashi, Rin, and Minato and basically going back to the way things were, except he and Kakashi would be friends.
Shit happened, and Obito got that completely crushed by Kakashi, whom with the gift Obito gave him and the chidori, killed Rin, Obit's dearly beloved. This shattered his world. He probably wouldn't have been so twisted had Madara not "suggested" the philosphy in the first place.
Sasuke... Yeesh, the guy gets his family whacked. His revenge against Itachi was simple then, but of course Obito had to go and actually fuck him up by manipulating him. He suggested that Konoha was ultimately responsible for his and his clan's suffering. With all due respect, the guy has reason to be on his warpad, all of his misery a direct result of an action that some people in the Senju-dominated Konoha made.
Itachi and Shisui are the only two Uchiha shown in the series with any great detail to not have a tendancy to bear extreme hatred towards things that do them harm, and you can appluad them for it.
All in all, the main reason Sasuke and Obito are the way they are, and not just crybabies, is becuase that's the way the story flowed. They were manipulated along the way. Kakashi never once has been shown to have been manipulated by anyone concerning anything involving the death of Rin and Obito, or any of his comrades for that matter.
