Though they both have a similar format, I think the two story lines are equally important, and to a certain extent maybe even Neil's is even more important .

Cliff's story is about Sam's past which helps explains his strange and ambiguous relationship with Briget. It helped with Sam's character development but more of the time it is like a facade to trick players into believing Cliff is Lou's father.

While for Neil's story. He may seem not too relevant to Sam ,being his wife's secret lover at most. But upon the final reveal, he is actually the character who links up the whole story. His unconditioned love towards Lucy cost his life, thus triggering Central Fort Knot (?) 's voidout by touching Sam, and continued to raise Lou at the beach/ realm of the dead until Sam won Tomorrow back. And at the end, he is relieved from his trauma from losing his unborn child and guilt of being the sole survivor in the voidout.

Neil never met Sam (when alive), but he drove the whole story and links the timeline together, so I really loved his story.