There have been accounts of both kinds of cat winning in captivity. These have included various varieties of tiger against mostly African lions. Also there have been battles between different sexes of the two. You can find several of these on the internet. Most of the videos I saw had the tiger winning.
The average male Bengal tiger is approximately 75lbs heavier than the average male lion. Of course for cats this big 75lbs isn't all that big a difference. Siberian tigers on the other hand are MUCH bigger.
Surprisingly the Caspian tiger was reported to be a very good fighter. Though smaller than both the Bengal and the Siberian tiger, it was very ferocious. Also it had a stocky build and abnormally large claws.
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