There really isn't an AMD equivalent to the i5 4590 right now, especially as far as gaming is concerned. The closest equivalent would be the FX 9590 aka an FX 8350 with a heavy overclock on it, and even then it would still fall behind in most titles. VR requires very high framerates, and AMD's current crop of CPUs are going to have trouble delivering that, they're at best adequate if you have a 60Hz monitor and don't want more than 60FPS on a consistent basis.
If you're willing to wait until late next year, you can see how AMD's new Zen CPUs perform and maybe AMD will have an equivalent to the i5 4590. If you don't want to wait that long, you're going to need to switch to Intel. Either way you're looking at a new motherboard, as both the current FX CPUs and AMD's future Zen chips will not work with your current motherboard.