It’s a lot closer than Narnia and the Bible–more like Paradise Lost; it’s the basic plot structure of the first part of the BoM, put into an elaborate SF society, with women, and lots of character analysis. The first volume is a 300-page expansion of the first 3 chapters of the BoM. Then he puts in a sort of inverted Christ-figure, but otherwise it keeps following the BoM’s first chapters – except for the animals on the new planet, of course, which I think he picked up from a line in Isaiah – until the fifth volume, which goes through the book of Mosiah in the BoM at high speed. The fifth volume is pretty weird, IIRC.
Most of the names are so similar as to be blindingly obvious, as Helena said. At least one is the same.
OSC essentially used it as a way to play around with what might have happened within the BoM history that we don’t know about. It’s a skeletal plot in scripture, so he fools around with character interaction and ideas about details and so on–and as he said to DangerDad at a signing, he wanted to put women in the Book of Mormon (which barely mentions them).
All you have to do is read, oh, the first few chapters of the first book in the Book of Mormon, and you’ll recognize it. It’s a short read, if you want to check it out.