I've never been much for doubles in rifles - shotguns are a different topic entirely But a double rifle only makes sense to me for dangerous game - for anything non-dangerous they're just worse than bolt actions. For dangerous game I think they're a relic of the colonization of Africa and India by the British and Germans and what rifles they had and the lack of thick skinned dangerous game in the Americas. Had the hunters of Africa been Americans, then .45 and .50 nitro lever action repeaters in longer cartridges would be ubiquitous rather than oddities owned only by a few enthusiasts. This may be heresy, but with modern bullets and loading techniques I'd say a suitably set up 1886 .50-110 is a better stopping rifle than a double .470 NE. If the .50-110s OAL was a couple tenths longer, there would be no question. Of course to do the same with cordite instead of AR-Comp it would have needed to be quite a bit longer... but such a gun would have existed if people and game were distributed differently. The bison just wasn't sufficiently dangerous to push hunters to repeaters, and was gone before nitro powder came in.
But if it has to be a double, I'd take the .450/400. I agree with Taylor that it's how big you have to go so you can safely engage any game in varied circumstances including brush without backup. Larger bores are useful only in very specific situations mostly related to the historical ivory trade. Yes, a .577 will put an elephant down longer on a headshot that misses the brain. But it requires a gun bearer meaning you really can't make much use of it. And the need to keep a wounded elephant down a long time while the hunter addresses their OTHER elephants is just not a scenario a modern hunter needs to worry about. So make mine a .450/400. With a recoil pad.