I think you can't answer such a complex question without further looking into the race. It's important to know the number of people in a said race, where they live, and what are other races that they encounter, how fast are their reproduction capability? Also, it's important to understand that the world isn't frozen in time. So apparently what would happen with the said fantasy race when a groundbreaking technology gets discovered or developed, or a large cataclysm starts?
A few examples.
If a fantasy race has a large population even with a larger lifespan, they would be basically like humans. Maybe a bit more quirky because the age dispersion would be probably more chaotic, but overall the same.
If a race is much smaller and has a way larger lifespan than it would be probably a race of individualistic beings.
Everyone keeps forgetting that humans aren't a united race. So the said race as well can easily fall apart or start waging war against their kin because they would have different life values, morals religion, etc. A great example is Eldar or Aeldari from wh40, they have a lifespan of a thousand years(I may be wrong here). As they achieved the pinnacle of technology and magic they started falling into depravity thus leading to a birth of a new chaos god. After this, most of their race was destroyed. While some of them survived they started following a strict set of rules. And the other part continued their depraved way of life.
And if you didn't think that I'm dumb and wrote stupid things, I have a question for you. Most people think about races who live longer, but what about races with a smaller lifespan? To those kinds of races, humans become long-livers. Will we as humans act differently? No, but they would think otherwise. It's a problem of perception of different mentalities. We may think that a High-elf who lived for five hundred years of which he or she spend three hundred years training with the bow and learning archery is haughty and contemptuous. But don't we think like that about athletes in a real-life? People who spent years of their life on training. There are genuine jerks, sweethearts but there are a lot of awkward people as well in real-life sports. Some people only sound arrogant but it's their passion that makes them say it. Or they may think that they are just stating facts, without any intention of offending anyone.