I don't think so.
Both XBOX's render at a pre-determined resolution then use a hardware upscaler to get 1920x1080. Frame rates should be constant regardless of HDTV res.
The PS4 however is rendering many games at 1920x1080 now.
Both the newer PS4 and XBOX ONE should be better at maintaining frame rates and hopefully target 60FPS more though a lot of new titles are still only 30FPS.
I know that the PS3/XBOX 360 were dropping to around 20FPS significantly in some games.