Yes, it will be better. By about 10% game dependent. Not only does the 3gb version have half the ram it also has less Cuda cores. Which in theory reduce the performance of the 3gb flavor. With that said, only in certain games is that difference apparent. Not all.
For decent 1080p 60hz monitor the 1060 3gb is fine. For max settings in most games, and slightly better FPS the 1060 6gb is better. The RX580 is also a consideration for that resolution.