I recently watched the BBC series ^^^ (it also co-starred our Richard Armitage as Sir Guy). The Robin Hood in that version kinda reminded me of Legolas in numerous ways. I think they are a close match-up.
ARCHERY
The BBC Robin Hood show lasted 3 seasons, during which I think I recall seeing R.H. miss a shot only once. He shoots his arrows a bazillion jillion times per episode (estimated), often several at the same time, and very often trick shots such as severing ropes from afar, shooting lobbed objects in mid-lob, shooting a net so that its contents spill out, shooting arrows into walls for use as footholds, giving out food by skewering the food item with an arrow first, then shooting the shishkabab harmlessly toward peasant villagers or his own men. He's also accurate at knife throwing. Compare: I don't need to spell out how awesome Legolas is with the bow, especially rapid-shooting. He can also shoot two arrows, but only does so at close range (the cavetroll, the mumak). In 3 movies, Legolas never missed. However, sometimes his shots were insuffiicent, i.e., the torch-bearing Uruk at Helm's D. He doesn't throw his knives but probably could if needed.
Number of successful shots: Edge goes to RH. He's had three seasons to gain the advantage over Legolas so the comparison is a bit unfair, but still.
Difficulty of shots: Edge goes to RH.
Ratio of successful shot per total shots: RH wins due to greater number of shots. RH and Legolas each have only one unsuccessful shot as mentioned above.
Ratio of hits to total # of shots: Legolas wins b/c he never missed as mentioned above.
Mutliple simultaneous arrow shots: edge to RH.
Archery edge overall goes to RH, but only because RH has had more screentime opportunities to use his bow.
ATHLETICISM
Legolas is quite the athlete, but so is RH. Legolas can swing-mount onto a moving horse, snowboard down the stairs while rapid-shooting, swing on ropes, climb Mumaks, slide down Mumak trunks, climb across cavetroll arms, etc. RH executes various acrobatic/gymnastics moves such as a back flip off a horse-drawn cart onto the ground, and others.
Edge: Legolas, hands down. A couple of flips here and there can't beat our very own stunt Elf extraordinaire.
MELEE COMBAT
Legolas is a versatile fighter who can stab with an arrow, or wield twin knives or even his bow. He can also throw punches and backfists, as seen at Meduseld while Gandalf was exorcising Theoden. When wielding his knives, he moves with lethal grace like Jet Li. However he doesn't do it much compared to RH. BBC's Robin Hood is a veteran of the Crusades and formerly one of Richard Lionheart's elite personal guards. This version of Robin can wield a scimitar or sword, or his bow and can fight unarmed. His skills at unarmed fighting are considerable and practical, not as pretty as Legolas but clearly technique-driven after lots of training. However if he gets angry, he makes mistakes, e.g., he nearly defeated Sir Guy in S3 in a fit of rage, but then he made a mistake resulting in falling and landing his head on a rock, and then got owned. However RH had more opportunities to get owned than Legolas did.
Edge: Both are skilled. Legolas' melee fighting style is prettier, but RH does more of it b/c more opportunities throughout 3 seasons. It's a draw.
Overall: it's a draw. However, if Legolas had the same amount of on-screen opportunities to showcase his archery, it would be a better comparison.