Re: 375HH mag or 375 ultramag?
I'm a new member, so if I make a wrong statement, I apologize. 375H&H is a fantastic cartridge, but unless you're a guide, it is not required for North American hunt. In Africa, law requires that you use .375 caliber or larger for the big 5, and needed for hippo. If you're hunting brown bear in Alaska and are nonresident, I believe that you need a registered guide. His license will be at stake, and he will not allow you to get into risky situation When you have an experienced guide to back you up, you will be calm and focus with the shooting. I've never found bears difficult to knock down quickly with the first shot. Just my experience, I think that elk can be tougher to kill. I think that 300 win mag and up would be entirely adequate for bear in Alaska and Yukon.
Now for Africa. The PH will most likely get you within 200 yards for the big 5, may be 300 yards for cape buff. Again, 375H&H will be suffucient at these ranges. 375 UltraMag is not required. In fact, I would choose 416 Rem over .375 Ultra Mag. Again, this is just my opinion.