I will attempt to answer this query with as little prejudice as possible, although for obvious reasons I strongly favor the bear.
First of all lets take a look at the tale of the tape on these two fictional heavyweights.
The Silverback Gorilla ("Gorilla gorilla")







Silverbacks are the strong,adult male dominant leaders of gorilla troops.
Size;
The eastern lowland gorilla is the largest of the gorillas, so I'll assume a lowland adult male silverback in his prime would be the choice of gorillas to oppose the Kodiak.
An adult male silverback weighs in between 300 to 500 pounds.(less then half the weight of the Kodiak)
Standing about five and a half feet tall (rarely a bit taller).

Diet;
primarily herbivorous
Gorillas have never been observed hunting or feeding on any animals other than invertebrates such as termites and ants.(not much in the way of a hunter/killer mentality that makes a good fighter)

Intelligence;
Gorillas are closely related to humans and are considered highly intelligent.(ok so he might have the brains to realize that this fight is not going to go well for him)

The Kodiak Bear ("Ursus arctos")







The Kodiak bear is a subspecies of the brown or grizzly bear.
Size;
largest bears in the world which grow to over 1,500 pounds,but the average adult male weighs between 800 to 1,400 pounds.
Between 9 to 11 feet long is an average size for a healthy adult male.

Diet;
Omnivore
Although Kodiaks are quite capable, they rarely will expend the time and energy to chase down and kill animals for food.(this doesn't hold true for the whole brown bear species though, as many populations of grizzlys hunt down large game such as moose and elk on a regular basis. The brown bear species is designed and wired to hunt large prey when the oppurtunity presents itself.) The primary diet for the Kodiak is fish, grass, plants and berries.The Kodiaks have a rather easy time of it as food is plentiful on the island, so they take what is easiest in copious amounts, because if a bear ain't hibernating or mating they are eating or looking for something to eat.(its what bears do, sleep/sex/supper, repeat)

Intelligence;
Kodiaks are concidered to be quite intelligent with the general concensus placing them somewhere between canines and primates.

Side by side comparasion;



So for the fight, lets say we have a 1100 lb adult male in his prime.
A bear that would be between 9 to 10 feet long, standing about 5 feet tall at the shoulders when on all fours.A bear that can move at speeds in excess of 30mph long enough to run down a full grown Moose.
Razor sharp claws on all four feet with the front paw claws as long as 4 inches able to disembowel a bull moose with a single swipe, but yet agile enough to grab a swift moving salmon from a stream effortlessly.
These forelimbs are incredibly powerful and deadly, the bear knows how to use them to their maximum ability.Now lets look at the teeth and mouth.Kodiak bears have very strong teeth: the incisors are relatively big and the canine teeth are large, the lower ones being strongly curved.Although their jaws are powerful they don't have the ability to break large bones with the ease of, say ,a Hyena.The bear's mouth is
spacious due to the shape of its skull. It would be able to engulf the entire head of a large silverback gorilla's head, shaking the gorilla like a ragdoll while ripping and tearing its body open with all of its claws.
The traditional 'bear hug' move would be the end of the gorilla.
The bear would most likely execute this move by a blazing fast lunge onto the gorilla, biting down onto its head or shoulder and grasping with its forelimbs
rendering the gorilla's arm strength useless.The bear could and would then proceed to rake the gorilla's body with its hindlegs, ripping its body open with the razor sharp claws, while puncturing and slashing with its forelegs as the gorilla attempts to escape the bear's grasp.
The bear's body is covered with long,thick fur, a thick layer of fat under its skin which could absorb the bites from the gorilla without taking much damage at all.
The rather short hindlegs of the gorilla don't have much in the way of offense, no claws, very short compared to the bear's and not much in the way of power to ward off the bear's assault.
The Silverback might have the intelligence to make a run for it, but it would be in vain as the bear can easily outrun the gorilla by 10 to 15 mph.
The end result would be the same either way if the bear is hungry, and like I pointed out, if bears aren't sleeping or mating then they are eating or looking for something to eat.
Conclusion;
The bear is hungry, it will dispatch (kill) the gorilla in a matter of a few minutes at best, and will proceed to eat as much of it as it can. (its what Omnivores do)

Then again what do I know?
Perhaps the fight would go more like this;

http://www.youtube.com/watch?v=CXzN3AyXR9w

We know that Silverbacks in captivity have had cats as pets, but what we don't know... is that in the wild, they not only have them as pets, but they train them for jihad activities.

With the bright and creative mind of the gorilla, he would win hands down without even breaking a sweat.
Enter his kitty on a leash. All he must do is get behind a tree quick enough while the bear is still sniffing out that strange new scent of nitroglycerin.

BOOM! Over...

I am sure that the Kodiak Bear will win the fight, in contrary to what most of my friends think here. I have plenty of reasons.

1. The bear is way heavier than the gorilla (1500 lbs. Vs. 500 lbs.) and in the animal kingdom and particularly in a deadly fight, that certainly gives an advantage; unlike in humans where in most cases, weight is a disadvantage (In other cases like in boxers and wrestlers, sheer muscle mass and weight really gives an advantage. That is why the weight categories are there). This is because animals do not become sluggish with more weight but become more powerful.

2. The bear is also way taller than the gorilla (almost double) and that is of great advantage too. Here, we must not forget that the bear too can stand upright. Kodiak bears are real giants.

3. The bear has sharp claws what the gorilla hasn't. It can rip open gorillas flesh several times with fast blows from its claws long before the gorilla can actually bite it. Further, it will be very difficult for the gorilla to bite the bear in sensitive areas (face, neck etc.) because it is much taller than the gorilla and its claws will not allow the gorilla to reach him easily.

4. Then the teeth. The bear, primarily a predator and then an omnivorous, has got sharper canines. But the gorilla, being a strict vegetarian, has somewhat blunt canines (clearly visible in the pictures above).

5. The bears are very ferocious (Being less intelligent than gorillas, they are more driven by their primitive instincts. They do not think, but react with reflexes). This intelligent is what makes gorilla a smarter but a weaker opponent.

6. Although the gorilla is smarter and knows the use of tools, but it is not sharp enough to discover use of appropriate tools during a fight, when every moment counts. It will simply not have that much time to discover.

7. Let's not forget that he bear is a natural predator as well whereas the gorilla is not. This makes a great difference in bloody fights.

8. Bears, although seem lazy and always panting, are actually very agile, fast and ferocious. They run very fast and fight relentlessly. Have you seen them catching fish? A polar bear can kill and skin a big seal within seconds. That explains everything. Kodiak Bears are no exceptions.

9. Bears have longer and thicker hair on their bodies. That protects them a lot from bruises, cuts etc. This is a big advantage.

10. Especially before going to hibernate, bears accumulate a lot of fat in their bodies. This is a great advantage from the point of view of continuing the fight for long without getting tired and recovering from the injuries.

The Kodiak Bear will definitely win.

Try it!

Thanks

9.

I got the gorilla...he's got speed, he's got cardio, he's got opposable thumbs, he can think on the feet. I put on a stocking cap and made him chase a chicken around in an alleyway until he caught it, and then I made him run up the steps in Philadelphia.

If he tells me to "cut it, Mick!" I'm going to cut it.

What were we talking about again?

Oh yeah, GORILLA FTW!
WAR GORILLA!

I would give it to the gorilla - sure he is the underdog, but his is the smarter of the two with brute strength like he's got, you don't need claws - you rip out chunks of flesh with your fingers alone.

Contrary to one of the earlier answers - battles in he animal world do not just come down to size - the big cats often take down bigger prey - albeit not carnivorous prey, but you get the picture.

The bear is big and powerful, but they aren't built for battling big agile primates - they are fish-eaters and scavengers. While a human might lack the capacity to take one on with its bare hands, a gorilla has all the tools that it needs to bag a big-ass kodiak bear.

With the bright and creative mind of the gorilla, he would win hands down without even breaking a sweat.

In true WWE style the winner will be the wild card that comes in as the battle begins.

The swat team/animal control.

Upon hearing that people are pitting these animals against each other someone would call the athorities. They would show up use tranquilizer darts and take out the beasts before the first fist or claw could land a blow. Humans have the advantage of superior technology an advantage that would show itself easily as people could even fire from cover, ending the battle before the poor beasts understand what is going on.