This study found that whey protein caused a greater increase in muscle protein synthesis than soy protein, especially after exercise. However, soy is still a good option for vegan/vegetarian lifters! Other studies have found beef-based proteins to be similarly as effective as milk-based proteins which can be helpful for individuals with milk allergies.
Reference: Tang, J. E., Moore, D. R., Kujbida, G. W., Tarnopolsky, M. A., & Phillips, S. M. (2009). Ingestion of whey hydrolysate, casein, or soy protein isolate: effects on mixed muscle protein synthesis at rest and following resistance exercise in young men. Journal of Applied Physiology, 107(3), 987-992.