We present high-precision V , B - V color-magnitude diagrams ( CMDs ) for the classic second parameter globular clusters M3 and M13 from wide-field deep CCD photometry . The data for the two clusters were obtained during the same photometric nights with the same instrument , allowing us to determine accurate relative ages . Based on a differential comparison of the CMDs using the \Delta ( B - V ) method , an age difference of 1.7 \pm 0.7 Gyr is obtained between these two clusters . We compare this result with our updated horizontal-branch ( HB ) population models , which confirm that the observed age difference can produce the difference in HB morphology between the clusters . This provides further evidence that age is the dominant second parameter that influences HB morphology .