If we're talking in terms of raw hardware performance, the PS4's graphics chipset should be a little below that of an RX 560 or GTX 1050. The Xbox One's hardware performance is lower still, probably closer to that of an RX 550 or GT 1030.
Of course, many games on these consoles only run at 30 fps, and many are upscaled from resolutions below 1080p, so in many games that kind of performance would be unsuitable if you wanted to run them at 1080p at equivalent graphics settings. On the PC, you do have access to graphics settings that can affect performance though, which gives you more control over how well a game runs on a particular graphics card.
I agree with madmatt30 that a GTX 1050 Ti would probably be a decent choice if you want to want graphics and performance similar to a console at 1080p, and the card's 4GB of VRAM should be fine enough for most games coming out over the next couple years. If you want closer to 60 fps at 1080p, then maybe a GTX 1060 6GB would be good. There's currently a shortage of AMD's cards in this price segment right now, causing them to be hard to find at reasonable prices, otherwise I'd also suggest the RX 570 / 580.