The Predator obviously has a pretty major technological advantage, so I'm going to lay out the contest three ways:
A). A straight up hand-to-hand brawl unarmed. There is precedent for this in the Predator's fight with arnold in the first movie.
B). A hand-to-hand fight with melee weapons. The Predator gets to use his wrist blades, whereas te Na'vi warrior is able to use whatever H2H weapon suits him best, or whatever Predator tech he is able to capture (think Danny Glover's character in Predator 2).
C). A traditional Predator hunt, where both sides are able to use whatever weapons are cannonically appropriate.
It would seem to me that the Na'vi is taller than a predator, and probably a bit faster and more agile. The Predator, on the other hand; definitely has an edge in terms of brute strength and durability.
I will provide the following links to wiki and avatar wiki for background information.
http://james-camerons-avatar.wikia.com/wiki/Na%27vi
Na'vi-
http://en.wikipedia.org/wiki/Predator_(alien)Smooth skin is iridescent, cyan color. Long tails. High cheekbones, feline-like ears and nose as well as large golden eyes. Bioluminescent markings that seem to follow the path of the circulatory or nervous system aid in identification and mood display. Average lifespan is unknown.
Despite skin color, Na'vi have red blood.[1]
Waist is narrow and elongated. The shoulders are very wide, creating a V-shaped upper back. The neck is long and body slender. Musculature sharply defined, giving no sense of emaciation despite thin proportions.[2]
Skeleton is reinforced with naturally occurring carbon fiber. Average male is 3 meters (9.8 feet) tall, females slightly smaller.[1]
Tail that can be moved and controlled like any other appendage and is used primarily for balance. It is frequently used to express emotion and is the basis for the Na'vi saying: "Watch your tail, Child!"
Average male has a mass around 162 kg. In Pandoran gravity (0.8 Earth g) they weigh 1271.38 N or 286 lb (compared to 1589.22 N or 357 lb in Earth's gravity.) Female mass slightly less due to lighter build and slightly shorter stature.
Three long fingers plus opposable thumb on hands; four toes on feet. (It should be noted that the Na'vi/human hybrid Avatars have five digits on both hands and feet.)
Highly evolved nervous system includes a "Queue" which resembles a long, rather ostentatious hair braid. This seemingly conventional braid actually sheathes a remarkably intricate system of neural tendrils that can be connected to similar structures of other life-forms. See Queue.[3]
They have roughly four times the strength of the average human.[2]
Reproduction mechanics similar to humans and other Terran mammals.[4]
The Na'vi are fundamentally different from all other Pandoran mammals:
They only have four limbs, while every other medium-to-large-bodied animals have a total of six limbs. (Prolemuris has four limbs, its front limbs branching out into two sets of "forearms")
They have only a single pair of eyes, while most other beings have two pairs of eyes, one primary set and another, smaller set.
All other animals have two nerve clusters extending backward from the head, while the Na'vi only have a single nerve cluster located in their queue. (Prolemuris also has a single cue, partially covered in hair)
Many animals possess twin air intakes on the shoulders that supply air and keep their internal body temperature down, while the Na'vi possess no such structures.
Predator
FIGHT!Predators are physically distinguished from humans by their greater height, arthropod-like mandibles and long, hair-like appendages on their heads. Their bodies are resilient to damage, capable of recovering from multiple gunshot wounds[1][2] and radiation doses which would be fatal to humans.[2] They are much stronger than humans, having been portrayed as being easily capable of outmatching a conditioned adult human male[1] and shattering solid concrete with their bare hands. They are also skilled climbers, and will readily move through trees[1] or across rooftops[2] in pursuit of prey. Though capable of surviving exposed in Antarctic temperatures for an extended period of time[3], it is implied that Predators have a preference for hot equatorial climates.[1][2] Their blood is luminescent phosphor green in color. Their vision operates mainly in the infrared portion of the electromagnetic spectrum; they can easily detect heat differentials in their surroundings but are unable to easily distinguish among objects of the same relative temperature.[1] A Predator's hunting helmet increases its ability to see in a variety of spectrums, ranging from the low infrared to the high ultraviolet, and also filters the ambient heat from the area, allowing them to see things with greater clarity and detail.[2] While they are capable of breathing Earth's atmosphere,[1] the creature in Predator 2 is seen using a breathing mask after losing his helmet. Their dietary habits are also mentioned in Predator 2, where it is revealed that the creature regularly visits a slaughterhouse every two days to feed on the stored meat there.[2]
Throughout their film appearances, Predators have undergone numerous design variations. In Predator 2, the main Predator was designed to look more urban and hip than its predecessor. Design changes included tribal ornamentation on the forehead, which was made steeper and shallower, brighter skin colouration and a greater number of fangs.[11] In Alien vs. Predator, the appearance of the Predators was redesigned to make them seem more heroic. Redesigns included a reduction in head and waist size, broader shoulders, a more muscular physique, piranha-like teeth on the upper jaw and dryer, less clammy skin to further differentiate them from the Aliens.[12] In Aliens vs Predator: Requiem, the Predator was returned to the sleeker design concept prior to Alien vs. Predator.[13]