What is GPU usage and CPU usage in the games you play with vsync disabled? If CPU usage is significantly higher than GPU usage you have a CPU bottleneck more than likely.
Going from a 4570 to a 4690 is hardly an upgrade at all. A 4770 would be a decent upgrade from a 4570. I doubt a 4770 would bottleneck a RX 480 in pretty much anything at 1080p or higher.