I started shooting .375HH last year about this time. I've found that this vaunted cartridge is useful for anything from coyotes to elephants. I shoot a Winchester Model 70, and its both incredibly accurate and also extremely versatile. Here in Colorado, I can snapshoot jackrabbits and hunt elk on consecutive days with this rifle using different loads.
The recoil depends on the stock you choose. It is certainly heavier than a .308, but not painfully so. One day I put over 70 rounds downrange off the bench (hardly a recoil friendly situation!) and was no worse for wear.
However, I own a .308, and love it. Longrange steel, elk hunting, a truck gun... what's not to like! That being said, when I go to grab a rifle, for some reason that .375 is ending up in my hands.
I got both...