Jack and Christian had one thing in common: their last name, Shepherd.
Shepherd is a noun which means a person who tends and rears sheep.
It also means a member of the clergy who provides spiritual care and guidance for a congregation.
As a verb, it means to tend to a thing or a task, or give guidance to (someone), esp. on spiritual matters.
Sheep tend to be docile, dumb, domesticated animals. Sheep is also a semi-derogatory slang for a mindless follower.
It a way, we can see both definitions in Jack and Christian.
The obvious connection is Christian to religion. In his death, as a spirit, he provides his son with care and guidance to get him to the right place (the sideways church).
Jack, on the other hand, is a de facto leader of a bunch of sheep (plane survivors) who need to tended (survival) and directed to the task (rescue).
But Jack is a reluctant leader. He does not want to make the big decisions. He is uncomfortable around people other than his ER staff. He was taught early on in his life that he did not have the emotional guts to be a real leader, the type of person who can make life and death decisions, and be able to live with the death ones. That is why Jack was delusional with his patients; that every case had hope and a miracle result. Jack could have been living in a fantasy world for a long time.
And Christian was a terrible father. As such, he was a pretty terrible angel. Angels are messengers from the after life who are sent to the realm of the living to guide people on the right path, to make the right decisions, and to change their destiny. Even in ancient times, powerful kings sought out the spirit world for guidance before battle. The righteous of the cause was as important as the army in the field. Christian showed up on the island as a ghost to shock Jack into remembering his childhood, and the associated guilt of not making up with his father before Christian died.
We would learn that several appearances by ghost Christian were in fact the smoke monster (MIB) or possibly even Jacob, directing Jack to find the cave (for fresh water). But it does not limit the possibility that the spirit of Christian could have been on the island (if his body was in the coffin). If MIB can only transform if a body was on the island, then Christian's body would have been present. However, in the sideways after life story line, Christian's body was not on the plane.
If Jack was the shepherd in charge of getting his followers home, then he did a fairly poor job of that as well. The island wolves picked off most of the beach camp survivors. Only Kate, Sawyer and Claire (and Aaron) made it off the island in the end. That is a pretty low batting average is survival (life) was the goal.
But if Jack was the shepherd in the land of the living, Christian was not the shepherd in the land of the dead. Christian was strangely the master of ceremonies at the reunion in the church, but Christian had no part in bringing any of the people to the church. As a dead person, he had a physical form (just like everyone else). He also had complete memories of what had happened to him. But we think he must have some background on all the others, because he told Jack that "they made" this sideways world. (Again, we don't know how anyone could create a private purgatory).
It was Desmond who began to awaken the 815ers in the sideways world after Charlie tried to kill him in a car accident. The hand on the underwater glass sparked Desmond to remember his island time then spark his investigation into the 815 manifest. In some ways, Desmond was the real sideways shepherd gathering the flock back together again.
One could go off on a wild limb and say that if Desmond was the after life shepherd, he played the same role on the island. Christian could have been "lost" on his voyage across the River Styx. He wound up as Desmond on the island, an angel in disguise. This was Christian's purgatory, trapped in the vessel of Desmond. How else could have Christian learned about Jack's island life, his trials, tribulations, loves, hates and ultimate death? Christian would have needed that information in order to create a "heavenly" landing place for his son in the sideways world.
As leaders, Christian and Jack appear to be cut from the same cloth. They believe that they have the skill set to lead their followers, but they have fatal flaws in their character. Christian follows the path of the easy way out of his issues; Jack has a delusional fantasy aspect of his dealing with his issues.
It also seems like a huge bother to create a complex sideways world with layers of new back stories just to give Christian the opportunity to tell Jack that he is dead. It seems more natural in our culture to see ancestors greet us at the pearly gates than send our souls into an island boot camp of soul torture, pain and suffering. Perhaps it took all the people in the church to tug the metaphysical rope to pull an obstinate Jack into heaven. The sheep had to corral the shepherd.