So I was having this same problem when exporting to an h.264 file. I was trying tweaks with small sections of the video and it always played back smoothly, but when I did the entire video it was choppy. I am not sure if this will help in your case, but I found that when selecting what to export, if I started one-hundredth of a second after the beginning and ended one-hundredth of a second before the end in a custom selection, my playback was smooth. I have no idea why or how this works, but it may solve the problems some of you are having.
Good luck!