It's all application, and hunter preferences. On certain species, a rapid, effortless second shot is a damn fine idea and the whole reason doubles have such a following where they do, but I'm changing continents with that one. On those same continents where a double is often held in high esteem among professionals, you'll find another group of professionals of the opposite opinion and hardware. Of the two PHs I hunted Lion with, one carried an FN Mauser .458, the other a .470 Nitro double, both were equally experienced hunting Lion and things otherwise that often require some quick reactions.
The moral to me? Shoot what you like and what suits your style, there are very few wrong answers, and nothing is best except what works for you. The often touted limitations of most choices are often baseless, such as a bolt action being slow, or the double (or lever or semi for that matter) being inaccurate. I know there are bolt gunners out there who can match or better me with my double rifle for speed. The semis or levers being unreliable, or pushing a shooter to take a poorer shot because of what's on tap? Also hogwash, I hunt wolves every winter with semis and there's no better tool, for me, for that job. I've suffered none of the supposed shortcomings of nearly any gun I try, but rather exploited the advantages.
In my opinion, pick the gun that suits your particular preferences, and don't sweat what the guy next door is using or thinks. In the end they all just spit out a piece of accelerated metal.