Depends
Really it depends upon what you mean by "versatile".
If you mean "versatile to take a variety of large game, from small large game to very large large game", then the answer is the bigger'n.
If you mean "versatile to take varmints, medium, and large game", then the answer is the littler'n.
But I do *get* the appeal of the .243 Win, and would have to vote that without more info. I love it. I figured if the Inuit kill everything up to and including polar bears with the .223, the .243 win, as a couple of steps up in power, is pretty much overkill for anything I'd run into.
The .243 is a bit flatter shooting out to around 300 yards... past that, the 7mm-08 is superior both in terms of trajectory AND energy. Since the vast vast majority of hunting shots occur under 300 yards, you gotta like the extended PBR of the .243 (assuming it has the oomph for what you're going after). With an 85-100 grain "hunting-construction" bullet and a brain shot, there ain't an animal on the North American continent that will have it bounce off or deflect - ain't a skull that thick! So therefore it also depends on how good and precise you're gonna place your shots, and how close you get, and how well you know your anatomy. Shooting game in the head at 30 yards with a "underpowered rifle" that you shoot well will result in meat on the table infinitely more often than a hail mary at 400 yards (i.e. a miss) with a 7mm-08 or any other loudenboomer you want to choose. Not to mention be more humane/ethical.
Having said all that, with the shorter barrel you mention, that fact favors the 7mm08, since the larger bores LOSE less performance from a barrel reduction.
But heck, why not split the difference and get a .260 Rem?
FWIW, Not counting muzzleloaders, my 3 huntin' rifle chamberings for the lower 48 are: .243 win with 90s (little deer, goats, sheep, antelope, etc.), .260 Rem with 120s-129s (big deer, little hogs, little black bear), and .280 Rem with 139s-150s (elk & Shira moose, big boar hogs, big black bear).
Of these three, recently, my go-to rifle is the .243 Win. While I do plan to make the .260 my primary rifle when I transition to it, as of now the .243 will get the call for big game - having said that, the only big game I'll be going after for the foreseeable future is whitetails.
My 3 huntin rifle chamberings, not counting muzzleloaders, for Canada/Alaska & Africa (so far) are: .30-'06 (big elk, moose, & caribou, small African plains game), 9.3x62mm (Yak, Bison, Brown bear, polar bear, leopard, lion, and large African plains game like Eland), and .45-70 gov't with buffalo bore ammo (large mean dangerous African stuff). Plan to add a .416 Rigby or similar at some point.