For what it's worth, I have a book by a Swedish girl who shot some Bengal tigers in India in the 1960's. She used a rifle, I think a Husqvarna .30/06, with a S&W K-38 for a sidearm. Thankfully, she never had to use the .38.
I know of one grizzly put down by a game warden whom it was attacking. He used an S&W M-66, with 158 grain .357 ammo of unspecified brand and type.
The polar bear in the NYC zoo was shot by a cop with a heavy barrel M-10 and lead HP ammo, according to Massad Ayoob. I asked him if he was sure that the ammo was HP, which wasn't allowed in New York cop duty then, and he assured me that it was. He's a member here, and may see this and expand on it.
Be aware that a frontal head shot on a big cat may cause the bullet to glance off of the rounded skull. A number of men were killed by lions in Africa for that reason. The mane also caused some to think that there was more forehead than there was.