R9 290x in general runs better at 4k, GTX 970 in general runs better at 1080p. For a 4k setup, you might want to consider the new R9 390 with 8gb vram, which runs even better at 4k resolution.
You should consider the newer updated Hawaii GPU found in the Radeon R9 390x 8GB which is faster and slightly more power efficient as well. R9 390X 8GB performs closer if not same with GTX980 in games. The 8GB frame buffer is future proof for 4k gaming. But you should remember that a single GTX980 or R9 390X is not fully capable to handle games at 4k resolutions with all graphics settings maxed out. You need to lower some graphics setting to get smooth frame rate.
You can overclock the 390 to achieve 390x performance. Should you want more performance you can get another one in the future for x-fire.
Let's not forget that specs wise the R9 390X is a bit better, even if there is a small difference I think there is a worthy difference between the two.