I think there is some good advice here. If you've got a .308, that is adequate for your elk hunting. If you want a pretext to buy a new rifle, by all means, buy a new rifle. If you are buying a new rifle, a .30-06 is not much different from your .308, why not get something distinctly different? While I hunt elk on public land successfully with a .30-06, I have a hankering to own a .338 Winchester Magnum. For my hunting -- modest sized bull elk (4x3 in 2009 and a 5x5 this October) and modest ranges (60 yards in 2009, maybe 200 yards or even less this October) -- the .30-06 works well. I know a lot of people in the area I hunt who likewise use the .30-06 with success. My elk hunting partner has used the .30-06 successfully for 20+ years. I've read ample support in books for the adequacy of the .30-06. Notwithstanding . . . I would like to own a .338 Winchester Magnum. Can I rationalize this desire? Not really. Partly I would like to have this rifle as an additional rifle to hand on to my son when I die. Who knows, maybe he would like to go big bear hunting some day? I do not desire to hunt these bears, but he might. While I think the .30-06 is adequate, I can imagine circumstances where I would be thankful to have the additional umph of a .338 Winchester Magnum. What if the shot is 350 yards, and it is late in the day. Will a .30-06 anchor the elk that is quartering away so I don't have to try to track it in the dark? There are a lot of ifs in that scenario. Generally I don't like to shoot that far, but maybe in this scenario I'm able to assume a prone position with a nice stable rest on my backpack? Yes, I know shooting such a powerful rifle in prone may have significant pain drawbacks, but if this is the shot I've got, I'm liable to take it if I think I can make the shot. Also, again, crafting the scenario in the imagination, if I have time to assume the prone position and set things up to my likeing, why can't I add some extra padding between the butt of the rifle stock and my shoulder, since I'm imagining a scenario here?
Anyway, it is up to you. The .308 will do the job. If you WANT to buy a new rifle, by all means do buy yourself another rifle. The rifle manufacturers need new gun purchases to stay in business. Get a rifle that is chambered in something distinctly different from the .308 is the main advice I would give you if you just need to have another rifle.