Best all-around is vague and almost meaningless.
By the OP's definition, strictly ballistic performance is accounted for with no representation of the size, weight, portability, action type, or use of the rifle, nor of recoil, ammunition weight or cost, or other factors. By this criteria, when such factors do not matter, a .50 BMG or one of the various proprietary .4+ caliber cartridges would rule the roost.
When other factors come into play, other cartridges have proven themselves to be much better "all around" performers.
In terms of over-all versatility, little on the American market can compete with the utility of the .308 Winchester. This round can be had in any action type from single-shot to pump action to semi-automatic, and everything in between. Most riflemen will find a properly set-up M1A, FAL, or HK91 clone can accomplish most of what they need a rifle for from personal defense to hunting and competition. For purely hunting, a scoped bolt action in .308 will humanely bag at most ranges anything that can be hunted on this continent, though it may not be ideal for grizzly. These rifles are of moderate weight with low recoil, they are generally accurate, and even today, not really that expensive to shoot compared to other full power rifle rounds. Components and ammunition selection is broad, the round is extremely popular, and again, ammunition and components can be found to accomplish just about anything, from competition to personal defense.
The case is efficient and the round does 99% of what the venerable .30-06 can do while being offered in a wider variety of rifles suitable to a wider variety of tasks. The .308 also has slightly less recoil. While the .30-06 is versatile and popular, it is mostly used as a hunting cartridge, and availability of rifles in that cartridge suitable for other tasks are suspect. In particular, while a FAL Carbine or M1A Scout can be loaded to make them into potent defensive carbines, few such options exist for the .30-06. And even fewer exist for other cartridges.
In particular, for all around use, I don't think anything much larger than the .308 can be argued. While some cartridges boast similar versatility on game, none of the magnums and few other cartridges can claim the broad base of knowledge, availability of ammunition or components, or the rifle selection to make them viable in other areas. Magnums in particular also have more recoil and are more expensive to shoot.
Likewise, while other cartridges, namely the .22 centerfires, can be loaded to shoot accurately out to 800 meters, few of them can boast the terminal effect of the .308. Shooting HPBTs from 155 to 175 gr, the .30 caliber rounds retain both velocity and energy much farther than .22 caliber pills and are therefore useful to far greater distances for anything other than punching paper. If you want to shoot steel, or game, the .308 will be more effective, even if it is only a more satisfying report on steel. And while other .243, .264, and .284 caliber target cartridges exist that boast better ballistics than the .308, these are more often than not require handloading or suffer from extremely limited commercial ammunition selection. Additionally, they are usually limited to heavy barreled bolt action target rifles, sometimes without even the addition of internal magazines. Because of this, they too lack the availability and versatility of the .308, and are nowhere near as useful "all around." Little is, which is why my M1A would be the last of my rifles to go, and why the .308 is the last of the cartridges I regularly shoot to leave the stable.