The Russian grizzly bear averages roughly 580 pounds. The Siberian tiger averages roughly 425 pounds. At normal maximum size, the bear can be within the 800 pound range and the tiger within the 500 pound range.
The tiger is, in my personal opinion, the single greatest terrestrial predator on earth. He is a lone killer of big game. The three top prey animals of the Siberian tiger are deer, elk ( called moose in America ), and wild boar. The Russian wild boar is himself a formidable adversary. These are the biggest wild hogs on earth, reaching up to 600 pounds. Occasionally, a tiger will acquire a taste for bears. In Siberia, there are two species of bears; the Asian black bear and the brown bear. The Ussuri brown bear is also called the black grizzly or Russian grizzly. Since the black bear can dart up a tree at the first sign of danger, more grizzlies are killed by tigers than black bears.
Tigers hunt juvenile bears. They are looking for food, not a fight. On rare occasion, an adult sow grizzly is killed. The grizzly sow normally weighs within the 300 pound range but can reach a weight within the 400 pound range on occasion. Tigers do not hunt adult boar grizzlies as prey potential.
The most likely location for a tiger vs grizzly fight is at a kill site. Some bears have been known to habitually trail tigers so as to usurp their kills. Such a grizzly is called a satellite bear. The remains of such sites have been investigated, but as far as I know, such an event has never been actually witnessed. According to the experts, the grizzly normally dominates such a site due to his size advantage. A typical boar grizzly normally has a weight advantage of roughly 200 pounds; but sometimes much more.
I know of only one documented case of a tiger killing an adult boar grizzly. The tiger is said to have been a huge specimen. This happened in Jankowski. I have found no documentation to verify. An adult male tiger was killed by a grizzly in the 1943 Amur River fight. Again, I can present no proof. In 2000, a boar grizzly went on a tiger killing spree. Among the tigers killed were 2 adult females ( according to Peter ). Here again, I have no proof to show.
We could fill pages with historical fights in captivity from ancient times right up to within our own century. In those fights, sometimes the tiger is victorious, sometimes the bear. But, fights between captive predators are proof of nothing. It is those encounters in the wild that have meaning.