Both bands are talented and worth listening to, but this should not even be close. Specific albums aside, The White Stripes are by far the more important band overall. They came along first, and co-started a trend instead of coasting on the jet stream that a pre-existing trend had already created. Beyond that, Jack White is both this generation's guitar hero and unapologetic purist...almost like he combines Eddie Van Halen's and Tom Petty's respective contributions to the 80s (albeit in much smaller individual doses). He's shared a stage with The Rolling Stones. That's important in that they allowed it (despite not owing anything to anyone or standing to particularly benefit from connections to anyone more current than they are...it was mostly out of respect) and that he had the historical perspective to make it seem fitting. The Black Keys are good, but won't matter in ten years like The White Stripes (specifically Jack White) will.