I've never hunted them but I think that Chester Golf got it right, Barnes TSX. With that much velocity I'd be concerned about tearing up a lesser bullet on a close shot. Doesn't seem to be much value in having a cartridge that can stop a close encounter it you don't have a bullet up to the job.
Come to think of it, this is the first time I've ever suggested using a premium bullet. What would you take, Western Hunter, if you were to go? I think I'd take a 338-06 loaded with 250gr Hornady RN or maybe a 250gr Nosler Partition.