Well, neither Ponyboy nor Dally handled Johnny's death "well"; however, the two still handled the death in totally different ways.
Ponyboy gets very close to falling into despair as a result of losing his best friend and reacts internally. There is even a bit of denial when Ponyboy realizes that Johnny just made an allusion to Robert Frost's famous poem (that the two had discussed together while on the run) by telling him to "stay gold." It is hard for Ponyboy to imagine that Johnny is now truly gone. There are a lot of tears from Ponyboy, who has always been a sensitive individual. The entire event makes Ponyboy think introspectively about the life of a greaser, ... and of greasers everywhere. There is an absolutely perfect quote that exhibits this realization of Ponyboy's character:
It was too late to tell Dally. Would he have listened? I doubted it. Suddenly it wasn't only a personal thing to me. I could picture hundreds and hundreds of boys living on the wrong sides of cities, boys with black eyes who jumped at their own shadows. Hundreds of boys who maybe watched sunsets and looked at stars and ached for something better. I could see boys going under street lights because they were mean and tough and hated the world, and it was too late to tell them that there was still good in it, and they wouldn't believe you if you did.
Dally, on the other hand, reacts externally and, as such, DOES fall into deep despair (and almost insanity). In short, Dally reacts in the only way he knows how: with violence. Dally takes his despair out on the world by robbing a store, threatening suicide (without a loaded gun), and as a result, "lets" the cops shoot him dead as well: as dead as Johnny is.
A similarity that is important to note, however, is that both Pony AND Dally love Johnny. One (Pony) has more of a platonic love of a best friend. The other (Dally) has more of a fraternal love of a brother. No doubt that poor Ponyboy, the one who is left, will never be the same.
Ponyboy loved Johnny like a brother. He and Johnny were the best of friends. When Pony finds out that Johnny has died, he breaks down and cries. Pony is a sensitive young man and he internalizes a lot of his pain. When Johnny dies this is what he does. He thinks about Johnny and reads a lot and he takes his pain inside. This is just the way Pony is and it suits him.
Dally on the other hand is nothing like Pony. He thought of Johnny as a little brother. He tried to watch out for him and protect him. When Johnny dies Dally takes it horribly. He is distraught over the death. He acts out and acts crazy. The thing about Dally is that deep down he is a good person, but he lets his tough guy exterior rule him. When he is confronted by the police we can see where this is going to lead, and it does. Dally uses his grief and pain to get himself shot and to end the torment he is in.
These two characters are so vastly different but are connected in their love for Johnny. Even after his death, Johnny is able to bring together everybody in their love and grief over losing him.
In the book The Outsiders Ponyboy was upset over Johnny's death. He was still not feeling well and having headaches, but he contemplated on his loss. Initially, Ponyboy has trouble accepting that Johnny is dead. He recalls just a short time ago Johnny telling him to stay golden. He had just been with him. Ponyboy won't let anyone touch him.
Dallas, Dally, externalizes his anger and loss. He can not handle Johnny's death. Johnny was the only one he had really loved in the world and now he is gone. Dallas robs a grocery store. He sets himself up for self-destruction. He calls the boy's house and tells them what he had done. In the end of the story, Ponyboy applies his grief to paper as he tells the story of the Greasers.
Dally has a gun on him but it is not loaded. The police cars are chasing after him as the boys arrive at the scene. Dally raises the empty gun and the police fire at him killing him. Dallas has committed suicide in his own way. He had wanted to die.
"Dallas Winston wanted to be dead and he always got what he wanted."(154)