It seems to me that Epicurus/Lucretius' version is clearly enough based at least in part on the observation that we do not see things being created from nothing, and therefore there is no reason to think that anything could be created from nothing by a god or by any other means. This kind of reasoning is discussed fairly clearly if I recall in "On Methods of Inference." To me that whole chain of reasoning is a fairly understandable inference of a deduction based on that which has been observed to be true. It's not just an assertion based on logic but one that is grounded in observation for it's persuasiveness.
I don't see Parmenides' version being in the same league as it does not seem to be based on observation - or is it? Matt can you reword it into something more plain?