This study found that using dumbbells during the overhead press was more effective than a barbell for increasing shoulder muscle activation. This effect was seen in all three heads of the deltoid and was further increased by performing overhead press while standing. Dumbbells appear to be a better choice for training the shoulders, but continue to add variation to your movements for optimal gains.
Reference: Saeterbakken, A. H., & Fimland, M. S. (2013). Effects of body position and loading modality on muscle activity and strength in shoulder presses. The Journal of Strength & Conditioning Research, 27(7), 1824-1831.