As said above, it's a bit difficult to exactly match the performance, given the PS4's unique CPU that has 8 cores, but very slow cores. And of course, even if you could match theoretical performance that doesn't mean real world performance would be the same, as console games will be better optimized for console hardware.
Here's an example build I might suggest if I was trying to make a cheap 'console killer': PCPartPicker Part List
GPU performance should be roughly on par with the PS4, CPU would be significantly better. That build deliberately cuts some corners for the sake of budget though, I generally think you'd be better off spending a bit more and getting 16GB of RAM, and SSD, and a 550/650W PSU. And possibly a GPU with 8GB of VRAM.
the original ps4 has a cpu similar to a fx 8350 but running at 1.6ghz, not the same cpu or architecture, but gives you a idea, is closer to a athlon 5150 but with 8 cores
the ram is 8 gbs but gddr5, like a gpu memory, vram
the gpu is similar to a amd radeon hd 7870, again, not exactly, but gives you a general idea of how powerful is
to outperform a ps4 these days a rx580 and a r5 2600 will wipe the floor with that hardware, except for the ram, we are on ddr4, gddr5 is faster but being the ps4 cpu slow and gpu slow, well, it ends up balancing nicely i must say, what a ps4 can do is very impressive