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.