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While Kamui seems detached and cold, Subaru, on the other hand, possesses a much greater capacity for compassion and kindness. He feels a sense of responsibility for those around him and he is far more willing to help out other people than Kamui. He brings a sense of humanity to the pair which Kamui generally lacked on his own. Subaru seems much like his X/Tokyo Babylon counterpart, though perhaps a little less damaged and a little more restrained in his empathy. He is certainly more friendly than his twin, and perhaps a bit more than his X counterpart, but in many ways he is still the polite, caring person he was before fate totally crushed him in X. Though he clearly has strong feelings for Seishirou (though not entirely hostile feelings like Kamui's), he also clearly cares deeply for his brother, which leaves him somewhat torn.
The single most important relationship in Kamui's life is his bond with his twin brother. Really, it seems he has nothing else in his life, but whether this is by choice or necessity remains a mystery. The cost of traveling through the dimensions is always high, but he was apparently willing to pay the price if it meant he could remain with Subaru. Obviously he also endures the years in Acid Tokyo waiting for Subaru to wake up and viciously protecting the place where he sleeps. His feelings for his brother border on the obsessive and could easily become personally destructive in the long run if he never tries to connect with anyone else. If Subaru were to die or leave him, he would probably fall apart or completely lose any sense of humanity. When he does lose Subaru for a while, he seems to be a lost child lashing out violently as he tries to cope with the pain and defend his brother's resting place. Still, there is something sweet about his absolute devotion and the intimacy they share as twins.
For his part, Subaru also seems to care about his brother. As Fuuma points out, Subaru can be particularly dangerous when his twin is in trouble. In fact, the only time in the story where Subaru reacts violently is when Fuuma threatens Kamui, otherwise he seems very calm and quiet. He does have a connection with someone else--Seishirou--which suggests that he is more capable of dealing with people outside of twin dynamic.
While Kamui may seem to be the dominate twin when he says "That's forbidden," when Yuuko suggests Subaru giving Fai his vampire blood in exchange for fresh water for the reservoir, or when he says, in reference to Seishirou, "I will never let him catch up with us." Certainly he seems to be claiming an element of control. Still, he tends to listen to Subaru when he tells him to wait. He may not have "allowed" Subaru to give up his blood, but he did follow through with the plan to which Subaru was prepared to agree. Although they appear together only briefly in the story, it seems like Subaru softens Kamui and keeps him in check. As suggested earlier, Kamui was like a lost child without Subaru. In a sense, Subaru is truly the more dominate person in their relationship, if there is such a thing. It might be that they are fairly equal in their influence.
The exact event that makes their journey through the dimensions necessary is never revealed, though it involves Seishirou in some manner. Despite the hardships, Kamui appears to neither resent nor enjoy their travels--they are a means to an incredibly important end, which is protecting Subaru. He does not seem to blame Subaru for their situation. In some ways it appears so attached to his brother that he could hardly resent anything about him. For Kamui, the problem is entirely Seishirou. Subaru, and his mission to protect him, gives Kamui's live meaning