I think horse1 has it pretty close. Besides the added "fun" of more blast and recoil, the chief advantage (in my own VERY personal view) is greater magnosterone bragging rights.
Whether are not a larger cartridge kills faster is open to debate,but it does offer some advantages.....
1- the Animal will have a more visual reaction to being hit
2- bigger calliber bullets are easier to hear the impact when you are the shooter( at least to me anyway)
3- Larger diameter exits and ussually mean a better blood trail if needed
4- On realy large game a better chance of acctualy breaking bones rather than shooting caliber size holes through them ( yes I have acctually seen this on Very Large Bear ,and on Moose bullets were Partions)
Maybe no other advantage, but an advantage none the less
