I'm currently writing a story where it plays a role. Here most longliving elves are very risk averse. To live 500 years or longer with a missing leg, or worse handicaps, is a drag. This also means they train for over a 100 years to get movements right, rather than humans youth who experiment wildly and have more accidents. But hey, they have the time.
In the lands of Atan the storytellers and singers know of many tales in which the Aleiyd and Varal appear. These two folk are mirrors to each other in how they deal with immortality. The Aleiyd choose disregard for times passing, only ever concerning themselves with the joy of the moment. In their understanding, nothing in the past nor in the future holds anything of importance, because everything becomes meaningless by comparison to the infinite tides of time. The Varal found meaning in the infinitesimal and became obsessed with the passing of time. Everything is of note to them and they desire to document it all: An account of the development of an ant-colony would for them be of the same-value as the collected history of a kingdom. In their stories they are no malicious actors, but they are seldom of real use for the hero. They serve as tests for the character, holding enticements to tempt them away from their quest and as a warning against detachment as well as obsession
In my world there is only one sapient species that outlives others by a significant margin. Dragons can live upwards of 500 years. They generally stick to themselves and think of things on a much drawn out scale. They avoid mingling with others mostly out of self preservation, as the encounters almost exclusively get violent and end badly. They still have a mortal understanding of death and loss though, and an early death for them is a great loss to their kind. As far as the unnaturally extended lives go there is a certain class of undead, that are priests of a death god, who can halt at the moment of death, remaining ageless and functionally immortal as long as their faith remains true and the gift isn't revoked. The oldest of these on record is the current serving hierarch of the faith, and he has existed for 923 sols. He is a scholar of history, and has explored whole lifetimes as various versions of himself. He has become a wise and humble observer, although he takes a rather objective and pragmatic view on events and decisions other people would consider more emotionally important.
The long lived observer trope is one of my favourites in that regard. So much knowledge and wisdom that yet would feel so alien to whomever he talks about it with because the perspective is just so different to your own.
It depends on the story I want to tell and the being that has it. With Elves, and other races. I overall prefer longevity, but if they are supposed to be immortal, it's functional immortality. For something more villainous I usually prefer true immortality* with an asterisk of being able to killed via an Achilles heel like destroying the one Ring destroyed Sauron. Absolute immortality I'd only use very rarely and would need to fit a theme certain theme without alternatives.
