The 500/416 will probably give you better penetration.
You will pay for that in increased recoil. It's a 500 case necked to .416. The .416 is a good long bullet that penetrates.

450/400 in either .411 or .408 is a good long bullet that penetrates. The recoil on the 450/400 3 inch is a lot less that the 500/416. At least it is to me!

You might search the forums on AR for post by "els".
His new Searcy 450/400 3 inch did a heck of a great job on the 3 elephants he took last year, He's now enroute to Africa this year with his 4540/400 3 inch.

I know you are searching for the "perfect" double rifle. After going thru this my own self and with others. I think you need to just buy the one you think will be best for you. That will be the best double rifle of all!