You can find .243 ammunition almost anywhere. While I don't think the 7-08 will "die", you still probably won't find it as often as you will .243.

If you're not hunting elk, the .243 will more than handle deer and anything below (varmints, etc.). Though I'm sure it's plenty adequate, I honestly don't see many people carrying 7mm-08s elk hunting. Even the fantastic .270 is considered by many to be "too small" for elk anymore - so, if you're thinking you're buying them a rifle that will last a lifetime, you're also banking that they don't fall victim to the marketing hype surrounding so many of these new cartridges (many of which may very well "die").

I opted for a .243 over a .308 when I had a choice at age 11. I've never regretted it. That rifle's still in my battery and has killed more prairie dogs than I can remember, not to mention a couple dozen deer and pronghorn, not counting what it's done when I've loaned it to friends to get their own kids started hunting. In college, I used it on elk (successfully) until I'd collected enough spare coin to buy a new .30-06. It promoted marksmanship over horsepower. I still have lots of other choices, but I won't carry anything BUT a .243 for pronghorn, and more often than not carry one deer hunting as well.

My vote's for the .243.