You’re leaving out an important factor here: Bombs.
Link doesn’t go anywhere without a few bombs. Using the famous bow/bomb trick, he straps some explosives to his arrows, takes aim, and shoots.
Tree bark and elf bits everywhere.
Right, it’s important which world this takes place in. That makes all the difference, I think. Yes, Legolas can see for 15 miles, but in Hyrule, the edges of the world, from desert to tundra, are what, two miles apart? I didn’t think about it, but if they were so far apart to be out of Navi’s range, Link would be toast. Not as fast as a goblin or orc, but it would happen. I assumed they would be closer than that; most of Legolas’s foes were.
In the end, even though Legolas has better dialogue, he’s a sidekick. Link is a hero.
A good plan but for one fatal flaw. (Well, two, because Link is kind of slow.) You can only have one magic-using item or spell in effect at a time. This means you can’t cast Din’s Fire while Nayru’s Love is going. If Link had Bombchu, he could slide a few dozen of those toward Legolas from medium range.
I don’t know. Five, six minutes? I did some research on these two for my last Halloween costume.
I just remembered. Legolas didn’t see 15 miles in the movie; that was in the book. In the movie, they were set upon by the Riders of Rohan when they were just over the hill. Clearly, the movie Legolas has some vision problems.
Eh, I think Link was designed more around the idea of being a hero to save the world from Gannon through multiple means. He isn’t just handy with a bow, but he is good with a sword and shield and can use some magic…and regardless of that he is the main hero. It doesn’t matter what combat abilities he has, it is his stalwart heroism and unbreakable will that makes him a good character.
Legolas on the other hand is just really freaking good with a bow. Sure, he has a couple of short swords and the will to face hoards of bloodthirsty orcs and what have you, but he is known better for combat abilities and elvish grace than anythign else.
So who would win in this duel?
Legolas.
I think too much is being made of Legolas’s vision advantage. Remember that the OP specified that the fight would take place in a forest; visual range will be limited by line-of-sight, rather than by acuity. Also, if Link has access to Nayru’s Love, Legolas is likely to waste all of his arrows while Link is invulnerable, given his insane rate-of-fire. Even if the fight doesn’t take place in Hyrule, I still say Link has the advantage.
Oh, and Wolfian? Dodongoes taste like chicken, while wraiths are, at their best, tasty but insubstantial. 
Link: I look so good.
Legolas: Arrowed!
Link: Ow, my skin!
FISH
Don’t forget Link can pick up boulders and other heavy objects. If he runs out of arrows, he can rip up the nearest tree and invent Hyrule caber tossing, with Legolas as the target.
But Lambas bread keeps better than Lon Lon Milk.
Legolas will be better nourished.
I don’t know, Soup. Lon Lon Milk will apparently keep forever in a good bottle, and it completely replaces all other forms of nourishment. Think about it, have you ever seen Link consume anything else? Besides, it heals you, which lembas wafers–however tasty they may be–don’t.
Da da da DAAAAAAAHHH!
You got some Lon Lon Milk!!! Now hold it above your head. It’s good for business.
I have to confess, whenever I drink milk, first I stick the bottle out in front of me. Then I dramatically chug it down, imagining five hearts filling up over my right shoulder. Then I wipe my mouth with the bottle hand.
I don’t drink milk in public anymore.
Well, I have an idea on who could win on this, but which Link are we talking about? Adult or Young Link in “Orcarina of Time”? Or even the Link in “Wind Waker”? The weapons vary in this case since there are so many different versions of Link that Legolas could possibly fight.
Now if it were Adult Link from “Ocarina of Time” then I see Link winning with his advantages in healing, magic, and weapons. He has 4 different things to heal with: Lon Lon Milk, red potions, blue potions, and green potions. He can use all of those for him to win in the fight. And all of the weapons he can use: swords, arrows, MAGIC arrows, hookshot, hammer, and a lot others.
If it were Young Link from “Ocarina of Time” then Legolas would win. Link just doesn’t have enough things to beat Legolas when he’s younger. He doesn’t have as many abilities, although he does overcome Legolas in healing once again.
Now Link from “Wind Waker” I see him beating Legolas as well, he can use all the items that the Adult and Young Link can use from “Ocarina of Time” and he can heal as well.
Legolas does have amazing skill at the bow, but he only has lembas for nourishment, not even healing. It’s only for more energy to keep him going for a little longer.
But as I said before, it all depends on which version of Link is being used.
I think Legolas would win in this fight. He’s older and more experienced; he’s been fighting for hundreds, maybe thousands of years now. Also, his reflexes and his senses are spectacular; he is an elf, after all.
Link just has some stuff he can carry around. Plus, he’s a puny little kid when compared to Legolas.
The OP said it’s Adult Link from OoT. And you forgot fairies. And Green Potion doesn’t really heal Link.
While Legolas is very old and experienced, Link kills monsters from the ancient world left and right. A more realistic advantage is Legolas’s ability to make the camera go in slow-motion; Link can’t do that without a special controller.
Though I really like both of the characters, I think Legolas might have a better chance of winning.
Link and Legolas has very good sight; that’s true. The thing is Legolas has also very good hearing. While in the Zelda games, Link always has the advantage of knowing when an enemy is near if the music changes. If this was taking place in a real time sense, there wouldn’t be any music to help him. So when he would try to throw bombs or use the hookshot, they would create a noise, Legolas would be able to pick up on the sounds right away and shoot in that direction.
I always assumed that Link actually does have good hearing, and that the way the music changes is a sort-of way of giving the player the same advantage. Link doesn’t actually hear it. Remember that Link can tell that Sheik is standing behind him in the cut scene in the Temple of Time, even though Sheik possesses ninja-like Sheika sneaking skills.
In the same way, Link doesn’t actually see the arrows encircling a Z-targeted foe; they’re just there to give the player an idea of what he’s sensing.
LINK HAS NAVI! She can tell him where the enemies are.
Legolas has been killing all sorts of creatures from Middle-Earth. He comes from Mirkwood, which was depicted as a pretty scary place in The Hobbit, and he went up against countless orcs, goblins, and Uruk-hai in The Lord of the Rings.
I think his reflexes are also better than Link’s. He’d be able to dodge arrows, flying boulders, trees, and such much better than Link could run from the arrows fired off by Legolas.
And the winged thing the Nosedrool was riding, with a single arrow, from a distance so great that the rest of the party just saw a black speck. If that doesn’t qualify as a horror from the ancient world, then I don’t know what does.
Well, we don’t know yet if the movie Legolas does that, do we? 
And yes, I know Legolas also kills ancient creatures. I’m just saying that the fact that he is an ancient creature doesn’t necessarily give him the victory. Link may be a kid, but he has…the Triforce!
Drumroll please for the dumbest answer of all time!
Link wins.
Link has a Chao. While just one Chao may not seem like much, Since he has a chao, he has Sonic the hedgehog on his side.With sonic, he has the other sonic characters on his side.With the sonic characters on his side, he has the genesis/Saturn/Dreamcast/Game Gear characters on his side.
Legolas has no such chao. But he got parodied in mad. So he has a crapload of Movie characters on his side.
Now, the fight seems pretty even, and it is.
Up to a point.
Since Link has sonic working for him, he has Knuckles the Echidna working for him.
Knuckles is the turning point of the match.
Since, as anyone who played Sonic adventure 2 can tell you, he has the most obnoxious music of all time.
All that knuckles has to do is play that music and everyone on legolas’ team WILL commit suicide.
Link doesn’t have long to savor his victory, though.
Link can hear the music, too, so he WILL commit suicide.
But still win.
I actually feel a bit embarrased knowing all the references in this thread.
Link would of course win.
However…
If Legolas could kill that stupid Navi (“Hey, c’mon!”) so I would never have to see the little annoying bug again, I think Link should let Legolas claim the victory.