Neither. I am told that the consumption of paleolithic vittles conduces to weight loss. Maybe it does. But I say unto you: What doth it profit a man to lose weight if he suffereth the clogging of his arteries? On the other hand, you are not going to take away my olive oil and nuts.
So I'm sticking with the Mediterranean diet as a via media between the extremes. But don't make a religion of this stuff. Brother Jackass needs to be kept in shape. Well maintained, he will carry you and your worldly loads over many a pons ansinorum. But don't expect him to convey you to the summum bonum.
Avoid fads and extremes. Where is the extremist Nathan Pritikin now? Long dead. A little butter won't kill you. Use common sense. Eat less, move more. Keep things in perspective. Just one pornographic movie can damage your soul irreparably, but one greasy double bacon cheeseburger will have no adverse effect on your body worth talking about. And fight the nanny-staters and food fascists every chance you get. More on this in the related entries infra.