I don't own a .338 Ultra, but I do own a .338 Win. Mag. I can tell you that the .338 WM is plenty powerful. It has killed everything up to and beyond the animals you mentioned.
Considerations for shots over 300 yards? Why ask? Don't get too bogged down with these numbers for the game you are intending to hunt. Based on my information from various guides, you will rarely shoot a brown bear or moose past 200 yards - if that.
Keep in mind that, to the degree that you consider the "numbers" important - that being the published energy and velocity numbers in ammo catalogs, although the Ultra is faster than the WM, if you get a more areodynamic bullet in the WM, then it will, say past 100 yards or so, be almost as quick as a less areodynamic bullet in the Ultra (like the Swift A-Frame).
Also keep in mind that .338 WM ammo, at least in the areas you intend to hunt, will more than likely be available than Ultra ammo - in case something happens and you need it.
Zachary