In modern bucket seats the risk of whiplash injury is incredibly minimal. Your head doesn't have the distance to travel far enough to hurt your neck. On the other hand, standing on the brake will cause both vehicles more damage and cause the other car to decelerate more quickly, causing the occupants to experience more acceleration in a direction in which the restraints are less effective (getting pressed into seat-belts and airbags hurt more than getting pressed into a seat).

Standing on the brake is simply shifting the energy around at the expense of the other party