If you're looking to buy just one rifle and be done with it I say the 338 is the ticket. its accurate, its powerful, and its big enough for anything on the North american continet. I see or hear people always ask: is my 270 big enough, or is my 30 06 enough , or do you think I can kill a moose with my 243.
My answer is simple: If you're asking then you have doubts yourself and you've answered your own question. On the other hand I've never heard anyone say: is that enough gun? when refering to the 338. Now I'm sure that I'll get flamed that the 338 is too much for a whitetail or a mule deer etc. And I would agree to a certain extent. A 338 isn't my first choice for a whitetail gun, but it certainly will get the job done. And I'm certain someone will say its too much recoil. well yeah it kicks, but my 14 year old 115 pounder shoots mine just fine so he's either really tougher or we're whinners
Now, I want to close by saying that picking one gun is boring! Multiple calibers is the way to go. I like buying a new caliber just cause I don't have one. heck, I own reloading dies for calibers I don't even own....YET!