I'm going to go ahead and jump in front of some future arguements resulting from my statement that 416's shoot nearly as flat as 375's. They do. As evidence, you can check out the remington ballistics sight (I'll post it). If both rifles, 300 grain 375 and 400 grain 416, are zeroed in at 100 yards, at 300 yards there is exactly an inch more drop with the 416 as compared to the 375. Basically, your 375 H&H will drop 20 inches at 3 hunsky, and your 416 will drop 21 in. at 3 hunsky.

To summarize, go with the big boy. You can take it long just as well as the little guys.

the sight, to cite... http://www.remington.com/products/ammuni...*RS416RA*R338W2

P.S. The 338 win mad shooting a 250 grain bullet is listed on the bottom below the 375, on top, and the 416, in the middle. You'll notice that the 338 win mag actually has more energy than the 375 H&H after around 200 yards. Doesn't mean it'll have the same penetration, but it's a real killer as well.