How Did the Men Crucified with Jesus Die?

The only Gospel that relates anything about the fate of the two criminals crucified with Jesus is the Gospel of John. The other three Gospels simply remark that Jesus was crucified with two criminals and do not elaborate.

Now, since it was preparation day, in order that the bodies might not remain on the cross on the sabbath, for the sabbath day of that week was a solemn one, the Jews asked Pilate that their legs be broken and they be taken down. So the soldiers came and broke the legs of the first and then of the other one who was crucified with Jesus. (John 19:32-33)

With their arms outstretched and their body slumped, breathing would have been very difficult, and so they would have used their legs to push themselves up to breathe. Once their legs were broken, they would no longer be able to do so. As the weight of their hanging bodies was transferred to their chest, breathing would become impossible fairly quickly. Death would come soon due to either suffocation or their heart would give out.