"on end" is an idiom. It means "without interruption". Example: "I drove 14 hours on end."
The two sentences mean the same thing, but the one with "on end" emphasizes the fact that the separation of the two people will be uninterrupted.
["on end" has another meaning, depending on the context. It can also mean "standing upright" (vertical). "When I saw the ghost, my hair on the back of my neck stood on end!"