I did the opposite. I upgraded my fx 6350 (4.8Ghz 1.455v) to an i7 4790k (stock then) and still kept my 7870. The only game I vividly recall exact numbers on was in BF4. Like you, I got 70fps+ (high preset 2x msaa), although I never had dips below 60fps with my shiny new cpu. Before it was 45-70 every game. That was the reason I got upgraded my cpu first. In any other game there was the normal range of ~20fps difference between max/min, but I could, and would, adjust the graphics settings to get that magic 60fps minimum.
I couldn't stand that no matter the settings, the minimum fps with my overclocked fx 6350 was trash.