In almost all cases of elves and humans co-existing, with elves having these archetypical long-life traits, elves live separate lives.
- Wood elves live out in the wild woods, i.e. where there is little in the way of human style civilization.
- Dark elves live in caves or other areas inhospitable to agricultural human life
- High elves tend to live in a utopian bubble with little interest in what happens outside of said bubble.
- In the Dragon Age series, elves are either tribals living off on their own, or they are in society's lowest caste due to racial tension.
Whatever the reason, elves tend to mostly live in their separate culture. Because if they don't, then the lack of cultural difference between elf and human renders the distinction (which most stories rely on) somewhat moot.
Living longer is not always better
The only thing I can think of to make humans able to compete with elves is that like how most other long-lived creatures, they mature slower just like orange roughy or whales.
Your assumption that living longer is flatout better is not necessarily the case. I'm going to use the example of Lord of the Rings here. Lord Elrond, while a strong leader, has more than one flaw stemming from the fact that he lives longer.
Elrond's first flaw is that he is holding 3000 year old grudge about humans. He treats Aragorn based on what Isildur did 3000 years ago. As much as Elrond is still a functional leader and all that, he is partially embittered about humans as a whole based on something that happens so long ago that humans pretty much consider Isildur a distant legend, not as a current guideline on morality.
Elrond's second flaw is that his long life makes him unwilling to respond quickly to events. He could have responded quicker to the stirrings of Sauron, but he did not. He let it play out further. He barely even intervened other than healing Frodo. Galadriel sent some forces, but Elrond simply left the continent altogether.
Essentially, Elrond is a less extreme version of Treebeard, who is both unwilling to intervene because "short term" things don't really affect him, and he is also glacially slow in any decision he makes, because he has no concept of having little to no time to do something, which is perfectly encapsulated by him saying:
“You must understand, young Hobbit, it takes a long time to say anything in Old Entish. And we never say anything unless it is worth taking a long time to say.”
Treebeard effectively dismisses anything on what he considers "the short term" as being not worth it.
Taking these two flaws into account, Elrond's state of mind is no different from the same type of "too old to learn new things" or "too old to get hyped about a new thing" you see in senior citizens in the real world. It is a normal fact of life that as you get older, you become more entrenched in your own ways. Sometimes because you want to do so, sometimes because you simply can't keep up anymore.
To further extend the previous point, humans' short lifespans (relative to elves) is considered a gift (= a positive) in Tolkien's lore. The whole page in an interesting read, but to summarize: having been given a short and temporary life, humans are considerably more driven to make the most of what little time they have, which is something the supreme beings specifically instilled in humans to distinguish humans from the more apathic and slow to respond elves.
Which brings me to your question:
How did humans biologically survive in my world from elf?!
Much like how teenagers and young adults adapted to the new invention of the internet much better than the generations before them, elves can be fatally flawed in that their extended lifespans lead to them statistically having very archaic views on the world, and they do not easily learn the new ways of the new world.
This puts elves at a disadvantage for anything that is considered modern, whereas elves are at a significant advantages for things that are considered old wisdom, i.e. tried and true knowledge that does not change quickly.
Therefore, as long as your society has a fast turnover on technological discoveries, humans will be able to eek out a faster adaptation to these new technologies.
The answer is long enough already, so I won't delve into the details of the theory of evolution here. The main thing I want to address is that the speed of a species' evolution directly stems from how quick their generational turnover is. The faster they breed, the more generations they have in the same timespan, therefore the more change both for mutations to take place and for the superior mutations to become prevalent in the species.
Very simply put, insects are evolving faster than humans are. And, by extension, humans evolve faster than elves.
Which is also an adaptability argument, just like before. However, this is more of a biological adaptability argument, as opposed to the previous cultural adaptability argument.