A 375 of either flavor is a fantastic, perhaps the perfect, general purpose round. While a double rifle certainly can be scoped and used as a general purpose rifle, a bolt gun is better suited to the purpose. A double rifle is ideal for close-in work where a quick second shot may be required, ie as a stopping rifle, which is rather a specialized task. Would a more specialized (ie larger) caliber be a better match?
that said, the odds of a client actually using it to stop anything are between slim and none; if a 375 double brings you joy, go for it!
I’ve no input regards the actual firearm to choose.