I think you have picked a very versatile combo there. The .308, while it is the same case as the .243, has a much larger and much heavier bullet going downrange that is going to do significantly more damage. It is a near equal of the 30-06 ballistics wise and the ol' 06 has taken every species of game that walks our continent. You just need to pick your shots on the larger game and you will be fine.
The .223 on the other hand, is a fine round for varminting, predators, and most any small game and some medium game as well.
If you were to get a short action Savage with 2 bolt heads, one .223 face and one .308 face, and equip it with 2 shouldered barrels (or even standard Savage type barrels) in .223 and .308, you would have a very versatile rifle that would do most anything needed in North America, as well as most other places as well.
And if you wanted to expand your versatility beyond what you already have, you could add a third barrel in .338 Federal or .358 Winchester and gain a little more thump for the larger game.
With a system like this, you could have one rifle to do most all your hunting with, and have a very capable rifle at that. A detachable magazine Savage could be made to mag feed both .223 and .308 based rounds with just a mag swap, as they have no feed rails in the action. All you would need are barrels and you could expand this system even farther and make it even more versatile. And then there is the other option, and that would be to add a WSM to the mix as well. A .300 or .325 WSM, or even a 7mmWSM, would add some serious reach and firepower to the system, leaving no game in North America safe, and most game in the world would be easily taken as well, with only the largest being out of reach.
I like the .223 and .308 idea, but I like the single rifle idea even more. Beware the man with one rifle, he likely knows how to use it!
Kenny