The PS4's GPU is about what a 7860 would be, if AMD would make one, with performance that sits in between a 7850 and a 7870. The GTX 660 has performance that sits in between the 7850 and 7870 as well, so it's actually a good choice if you're trying for a PS4 GPU equivalent.
Unfortunately for you, Console games get quite a bit more optimization than PCs do, and devs can do lower level optimization on a console than on a PC, so generally you don't need just a GPU that's "as good" as what the console is using, but one that's a few steps better, if you want to match performance.
Your system will be interesting, since the performance differences we'd see from a system like this vs a PS4, will be almost entirely due to the superior optimization games have on the console side. I'd imagine that the gaming performance will pretty much always be a little worse, to quite noticeably worse than the PS4s performance, but tend to the "a little worse", since PC optimization should be easier this time around, with consoles having architecture that's more similar to the PC.
TLDR: Your system should perform a little worse than a PS4.