First off...
1.) The R9 390 is faster than the GTX 970 so your problems would likely be worse with a 970
2.) The R9 390 has more than twice the amount of Ram of the GTX 970 so that is another bottleneck eliminated.
You are not providing enough information for us to provide you advice.
What CPU do you have? How much Ram do you have? What specific game(s) is lagging? What is the resolution of your monitor(s)?