Why the two different words; do they have subtly different meanings?
Necro- usually refers to things that are dead. Thanato(s) is the event and personification of death.
Ah, I see the distinction. It makes a big difference since I was imagining a despotic tyrant (think Stalin only even worse) who maintains his power by killing huge numbers of people. He would boast by calling himself the Thanatarch rather than the Necrarch, the latter would imply that HE was dead.
Well, the necro-whatever might not be dead itself, but it would be defined in terms of a relationship with dead things: necromancer, necrophiliac.
But death itself, that would definitely be Thanatos.
Necrarch = Lord of the Dead. Thanatarch = Lord of Death. Presumably either one would be scary, but the latter seems more… active.
Your tyrant would be more likely called a thanatocrat. The -archy words generally refer to how many rulers there are - eg: none in an anarchy, one in a monarchy, two in a diarchy. The -cracy to whence the power originates - eg: from the people in a democracy, from religion in a theocracy, from wealth in a plutocracy.
So, someone who gains power through killing would be a thanatocrat - one who rules through death.
“Um…wow. That’s really, really, something. What do you call your act?”
“The Thanatocrats!!!”
Or, use the full version of the suffix: Ne’crarchos, Thana’tarchos. The ’ shows intonation.
Mmm, I dunno, Tengu. I think you’re conflating structure with teleology.
Democracy is not rule implemented by means of the people, nor theocracy rule implemented by means of a god. They are, at least in theory, rulerships of those bases. Willful power–kratos–resides there. A thanatocracy in this sense, is a government that obeys a willful Death, or perhaps colloquially a culture pervaded by and subject before death. The government does not employ death. Similarly, a necrocracy would be, in theory, the implemented will of the Dead.
But none of that is what I meant to suggest would be implied by the titles Necrarch and Thanatarch. I see the Necrarch commanding the dead (“Go forth! Seek brains!”), while the Thanatarch embodies or at least wields death actively. By scythe or otherwise. The terms don’t justify their positions, the way “democracy” implies its own rightness–they just describe what they do.
Anyway, I think Thanatarch sounds tuffer, which may be the overriding criterion. 
Hey! I like that, more name-like.
Would the emphasis be NEcrarchos, thaNAtarchos, or would it be neCRARchos, tanaTARchos?
As I said, the -cracy words refer not to who rules, but from what source they derive their power. (At least nominally so.)
The power in a democracy derives from the people, but it lies in the leader they selected.
The power in a theocracy derives from a/the god(s), but it lies in the leader who successfully claims to have been chosen by the god(s) in question.
Etc.
NEchrarchos and ThaNAtarchos.
Although the modern Greek version of the suffix would probably be more fitting: NeCHRArhis and ThanaTArchis.
This article in today’s NY Times about Chilean autopsies refers to the person who performs autopsies as a “thanatologist” (a word I’ve never heard before).
dictionary.con defines it as: