Not being a smart ass answer but the average PH uses a magazine rifle quite simply due to economics and availability.

Of those that do use doubles I would guess, and from those I know, that .470 would be the no 1 choice.

The reason is 2 fold, ammo availability for this round is better than for for some of the more esoteric calibres, by this I mean in Africa not in a London or Californian gun shop and secondly a resurgence in popularity in Double rifle has seen an ascendacny in the popularity ofthe .470.

In perormance the .470 is probably no better or worse than any of the .450 -.475 class rifles, just more readily available in resonable poriced contemporary rifles.

Searcy, Merkel, Chapuis all make field or ordinary grade rifles with no frills that offer an attractive proposition to an African Hand and it is these rifles that are becming more and more popular.

you will however still find the odd PH with an Original Rigby rising byte rifle or a Holland Royal, and other famous makes from the past, they are still out there giving good service and have been given a new lease of life with modern ammo.

But as you posed the question "most popular" then I think in a double that .470 is most probably the one