I've hunted with the same scope for 20 years--a fixed, 4-power Leupold.
I am a big-caliber guy, who's used the .375, the .416 and the 450-400 and loves them. I think 200 yards is a fair distance for the .375 H&H, although with cast bullets it will perform a bit more like a .45-70. No biggie--great target practice.
As for the bigger vs. smaller scope magnification, I fall squarely in the "less is more" camp. A larger-magnification scope will help you *see* better, it won't help you hit. When you're on a bench, this is good, while when you're shooting off-hand it can be (and often is) a liability.
Seeing the waving and bobbing of the crosshairs at (say) x12 make many shooters develop bad habits--like tensing up, holding their breath for too long, etc. This won't happen with a low-magnification 'scope.
Anyway, just my opinion. Get what you like and shoot a lot.
Tom