Both.. can't die and can't age.. I think half of us here can become recipient of immortality someday soon.. but if you are already 90 years old.. would you want to be immortal in 90 year old body forever.. maybe transferring to another body would be a good idea.
However, something concerns me. Is there any evidence at all that some aliens in the past improved our genetics so we were able to diverge from other animals and became self aware? Because if we were created as slave race... remember the warning.. "The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live for ever".. let's say someday we improve another planet with slave lifeforms, do we want them to live forever..
In other words, if we were designed and our alien creators didn't want us to live forever.. then before any of us can become immortals.. we may have to fight an intergalactic war first (or Earth sabotaged before we can even go up)?