The most versatile cartridge is often discussed when magazine editors are short on articles to fill the pages. American Rifleman's top 10 rifle lists caused some hype for sure. The issue is too many variables. They reviewed rifle-cartridge pairs as opposed to rifles and maybe cartridges the next month. The average reader would disagree with one or both elements.
Anyway, the most versatile big game cartridge is by far the .270 Winchester. For years and years it has but down big game time after time all over the United States. The magic of the .270 is the bullet velocity/weight/frontal area combination. The 3,000 fps mark allows any bullet to perform as intended and 130-150 grains is plenty of weight. The magnums out there can out-perform but not without more powder, more muzzle blast, and more recoil.
The most versatile varmint round is the .243 Winchester. It's a necked-down version of the .308 just like the .260 Remington and the 7mm-08. It can do the varmint thing with 50 grain bullets and covers the bottom spectrum of North American big game with 100 grain bullets. Not to mention that the .243 is a competent competition round. It has even been showing up at 1,000 yard matches with the 6.5's.
A rifle should be judged as a rifle, not the cartridge it throws. The Remington 700 wins my most versatile vote. It has been around my entire life and continues to kill animals and bad guys world wide, with the help of a skilled marksman and quality optics. It has good out-of-the-box accuracy and may be the most popular custom rifle platform save the Mauser 98.
Most significantly, the best rifle is one that is adequate for what you are doing and shoots where you look. If you don't know what I'm talking about keep looking.
If you're bored to death now just check out this picture of Ellie.