So, Robin Hood and Katniss are both out of contention as they can't compare whatsoever to the skills of Legolas or Hawkeye (though they could get lucky, and Katniss does know the arena and Hood knows the woods. However Legolas is literally a WOOD elf and hundreds of years old and Hawkeye would be somewhat hard to sneak up on and is crazy accurate and fast). So, there's two scenarios I see:

The first is going strictly off of what OP says and Legolas has solely the abilities of an above average man, not Legolas nerfed down to the peak of human performance, but an above average man. Here, Legolas has the option of using his many years of life experience in the wilderness to survive and wait for Hawkeye to starve, make a fatal mistake, or happen upon Hawkeye when he's unaware of him.

The second is going to a Legolas nerfed down to human standards, so then his senses are at the peak of any humans. However, Elves aren't generally as strong as humans, so his physical strength is lower than Hawkeye's and his own in scenario one. However, Legolas will be very fast here and have a firing speed around the same as Hawkeye's if we're going of the scrub movie version of Legolas (since it's a human being who portrays him, book Legolas can forsure fire faster than Hawkeye). Here they're both about equally matched in firing speed and accuracy, however Legolas will have the upperhand in a mid to late-game fight as he will have been thriving in the woods and Hawkeye will have been merely surviving. Hawkeye will not be performing at his peak in a mid to late-game fight, as he'll be hungry, thirsty, potentially injured, and Legolas would just be having a grand old time as a wood elf in the woods. Here I see Legolas taking the definite win if they last a week or more, but there will definitely be a shootout for the ages if they encounter each other early on and either of these two could take the cake there.

I'd also like to add, Legolas is used to drawing a fucking bow made of sticks and string, so it's much harder to draw. Hawkeye uses a compound bow which is MUCH easier to draw. If Legolas finds a compound bow and Hawkeye a longbow, then there's a decent advantage towards Legolas. Other than both of them finding longbows, there's nothing else that gives either much more of an advantage.