OLED vs 4K tv choice

I am looking to spend about $2k on a new TV. I have a decent 55 in. 1080p LG LED smart tv thats about 2 years old but, I am wanting to get in on either the new 4k or OLED stuff. I know my budget doesnt allow me to get something real great but I am just wanting the most bang for my buck. Anyway to my question...I am wanting this TV for playing PS4/xbox One thats really all that matters to me. Also I am wanting at 60 or 65in. I am wonder which would be better for this? With the myriad of choices out there it is just all too much to try and wrap my head around and make an informed decision (almost everyone has a differing opinion on the matter and the technical specs are just too much). I have been leaning toward the 4k TVs because they look incredible in the stores but, I am unsure of how well the up conversion will work since I wont be viewing any native 4k content (since its just not really available right now). I appreciate any advice you may be able to provide thanks.