Take most of the 'gods' of the ancient world- Zeus, Thor, YHWH etc. and see the matching actions and qualities or their treatment of humans. How is the god Zeus and the co-god Hades much different than God and Satan in Christian theology.
Well, for one thing, None of those Gods gave of themselves for lowly humans, none of them, gave their only begotten Son, none of them came down to US because we can never go "up" to Him, The Gods of Greece and the Viking gods cared little of man, man was their play thing and they have to prove worthy of the Gods love, the Christian God gives his love freely.
As for God and Satan, the obvious parentage thing aside, Satan doesn't really "rule" anything and certainly doesn't rule Hades.
Sure he is called the ruler of this world a few times, even by Christ, but he rule ended with Christs death and ressurection and he rules only those that have no belief.
Compare what happens in the Greek's /Underworld to what happens to unbelievers in Revelation.
Hades had many parts, including the allysian fields where the heroes went, but I think I know what you mean and yes, of course there is a sembelence, afterall, the writers were writing to an audience composed primarily of former pagans that were very familiar with "Hades" so they would use imagery that they could relate to.
Just as we nowadays would use the Jersey Shore show to prove how the world will end soon.
:)