The fact that a steak contains practically no antioxidants whatsoever is not the worst thing about it. Rather, it's the acrylamide (a carcinogenic substance) created during the cooking process. The charred areas you see on a steak - as well as other foods - contain high amounts of acrylamide. That combined with almost no antioxidant power make the typical beef steak one of the worst foods you could eat if you care about health benefits.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH Jan 2010