Big cats are the worlds most efficient killers, and the tigers are the biggest. Cats also have a highly attuned nervous system that makes them more susceptable to the shock from a high velocity bullet than other animals of similar weight. Fast bullets tend to fail in thick cover, and unfortuneatly that's where the tiger will probably be found.
I think I'd go with my .375 Ultra and plan on using a hot loaded Nosler 260 gr AB's if an open shot was possible, but for hunting in the thick stuff I'd fall back on the 380 gr. Rhino.