I don't think that souls in this particular in-game universe behave the same way that many of us would intuitively expect. Your sense of 'self' is largely a function of your memories, and most memories don't remain on a soul after it's returned to the lifestream without a good reason (i.e. powerful unresolved regrets, or Kairos' aetheric manipulations). Although I wonder what happens to all these memories. Perhaps there's a lifestream primal like FFVII's Minerva who sits around jotting all of them down somewhere.

Either way, if a soul does come back and there isn't one of those extenuating causes for retained memories as above, then it's a completely new entity. Who knows, perhaps a dragon soul might just spontaneously fragment in the Lifestream and spontaneously turn into 14 Elezen the next time around. I don't think that the native/alien distinction really matters either way, because it's just aether at the end of the day. I seem to recall something in one of the UT cutscenes that talks about lifesteams in other worlds, but I can't track it down at the moment. I might have a look later.