This study found that barbell deadlifts have a mechanical disadvantage which forces hip and back muscles to work harder. However, subjects were able to lift more weight in the trap bar deadlift which led to more power production. Use both types of deadlifts in your program for optimal muscle and strength gains!
Source: Swinton, P. A., Stewart, A., Agouris, I., Keogh, J. W., & Lloyd, R. (2011). A biomechanical analysis of straight and hexagonal barbell deadlifts using submaximal loads. The Journal of Strength & Conditioning Research, 25(7), 2000-2009.