Both animals are at the very top of their respective environmental food chains in terms of being the top predator (excepting humans). If they were forced together (say in a nature preserve) would these top predators be afraid of each other, or just curious, or … what? How do unfamiliar top predators react when confronting each other?
How about the say question with a Grizzly Bear and an African Bull Elephant? Would the bear have enough sense to be afraid?
My money is DEFINITELY on the Grizzly, and here’s why… endurance. Cats are notoriously poor “long distance” athletes. Down here in Australia, feral cats can be run down into a state of utter exhaustion after just one mile in the open. Sure, they’re fast - for a while - but when they die, they die big time.
Contrast this to a Polar Bear for example. Those suckers apparently can swim up to 100km a day. They can run surprisingly fast too - but more importantly, they can run a long way. Their natural habitats are huge.
In terms of weaponry - I’d say it’s about an even fight. The tiger could probably get a slightly better throat wound going - but I imagine that would merely invite a death hug from the bear. Both of them could inflict some pretty gnarly wounds on the other doubtless - but the Grizzly could keep it up for 10 minutes easy as. The tiger would almost certainly be exhausted after 3 minutes I daresay.
I don’t think any top of the line predator fears anything. Shoot some prey animals fear nothing. Have you never been attacked by a bluejay when you approached to close to it’s nest?
I’m sorry I should have been more clear. I’m not looking for the winner of a bear/tiger fight. I’m wondering what the inital fight or flight reactions of these top predators would be toward each other (a s unfamiliar animals) given that there is nothing that typically challenges them (other than another bear or tiger) in their respective ecological niches.
Maybe I’m missing his point, but I don’t think astro was asking which animal could take the other in a cage match. I believe he was asking what the instinctive reaction a large carnivorous predator would have if confronted with another lcp which it was unfamiliar with. Due to the narrow enviromental niche this type of animal inhabits, it seemingly wouldn’t have any inherent genetic instinct for this type of encounter.
I saw a clip on the animal channel of a tiger and a bear being introduced to each other. I don’t know what kind of tiger nor what kind of bear, but they were close enough to each other to touch noses. It looked like they were sniffing each other’s faces. The tiger appeared to be very young, FWIW. The clip was short; I don’t know what the context was or what else happened.
My guess, based on nothing but what I know about zoology and such, is that the other predator would not fit the creature’s programming as to “prey.” Thus, they probably wouldn’t attack each other right away. If there was no aggression shown by either animal, they will just go their own ways. Toss something they both recognise as “food” into the mix, and then you will see some competition! 
I think that both would recognize the other as “large”, “unfamiliar” and “not fleeing” – all suggesting wariness (though the exact reaction may vary by “temperament” - i.e. individual personalities). Either might be able to tell by smell that the other is likely a carnivore - another sign to be wary. I agree with earlier posters that they probably would avoid each other unless the circumstances forced them to conflict.
I’m not even sure that the presence of a prey animal would be enough to make them conflict (they’d probably aske themselves “Am I that hungry?”) – territoriality might make them challenge one another – but a) how would you rig it so that both thought “this is my turf” while never encountering/scenting the other or signs of the other (e.g. scat); and b) almost all animals are more territorial towards their own species, and tend to ignore other species (humans of some subcultures are an exception – e.g. urban Americans are rather intolerant of unfamiliar individuals of almost any species “on their turf” and more tolerant of unfamiliar individuals of their own species who make the proper greeting displays)
Dominance may also play a role after a kill is made. Lions and bears tend to chase off smaller predators who make a kill (You know that classic sunrise scene where the lion is eating a carcass, as the jackals skulk a short distance away? Well, night vision has shown us that often the jackals made the kill, and the lion chased them off – lions are lazy, and rely on their size; lionesses do more hunting) I don’t know enough about the behavior of Siberian tigers to speculate.
I have yet to hear of a grizzly being frightened of anything. They’re psychotic, nasty killing machines that will attack nearly anything, including inanimate objects, if it pisses them off. Or not.
Why would a Siberian tiger never have seen a bear? Why would you assume that a grizzly had never seen a big cat.
Siberian tigers commonly share habitat with bears and grizzlies commonly share habitat with cougars. The conclusion seems painfully obvious. The tiger would assume the grizzly was a big bear and the bear would assume the tiger was a big cat.
Exactly how it plays out would depend on the fitness of the participants. Tigers will hunt injured or weak bears but they will simply ignore healthy individuals. Bears won’t hunt large cats AFAIK.
Chances are the animals would take a long curious look at each other and then walk off. It’s not like they’ve never seen very similar animals many times before.
Grizzlies aren’t even as big as the Siberian variety of Brown Bear, the Kamchatka Bear. So it might think it was a small bear!
But to the bear, it’d definitely be a big pussy
If there were a flaming hoop present, I would give the advantage to the tiger.
Bullshit. The tiger might be able to jump through the hoop, but could it drive a little car through the hoop. I think not. The tiger is toast.
Hmmm…I considered the little car, but I put more credence in the embarrassment the bear would encounter wearing the little hat whilst driving.
Then again, the tiger would probably be wierded out by Survivor’s Eye of the Tiger playing in the background.
Hmmmm…
They would not see each other as predator or prey, but I’m guessing that they would see each other as competition. Each one would want the other off of its turf (assuming they both try to claim the same turf, which I think is implied by them meeting in the first place). So they would probably start by trying to intimidate each other, growling, showing teeth, making themselves look bigger, etc. If that was enough to drive one off (most likely), the other would be just fine with that, and end of encounter. If it wasn’t, they might start fighting. Whichever one has the advantage (I won’t speculate on that), it would probably quickly become apparent to both combatants, and at that point the loser would break off the fight, and again, that’s the end of the encounter. It would be highly unlikely that they’d fight to the death: No hunting ground is worth that.
As for an elephant and a large predator, I don’t think that the predator would even consider challenging the elephant. It’s too big to prey on, and they don’t compete for resources. The elephant might strongly encourage the predator to stay away from the calves, but other than that, I think they’d mostly just ignore each other.
:: immediately shoots both tiger and bear dead ::
What?
In general land carnivores don’t prey on other carnivores*. They can and will drive them out of their territory, however. In the OP’s case, I’d say if the hunting was good, they’d be wary, and if either got too close they’d bluster and threaten.
*one reason why I think that humans aren’t usually prey, and that there have been several attacks on vegans by cougars. The average human smells like a carnivore- and thus doesn’t smell like prey. (I know my vegan freinds insist that I “stink of meat” and if their noses can tell the difference, a cougar’s certainly can)
I think the tiger will run from the bear due to its bulk. Everything else aside the bear is probably bigger than the tiger, especially if it stands up. I think the tiger might recognize that and keep its distance.
I smell a reality show cooking, PPV style. 
Discover channel already had a show pitting the Siberian Tiger versus the Grizzly Bear. In a virtual computer the face-off, I recall that the bear slapped the tiger senseless.