Frames are an index of time, so if you get that time index of 2 frame lag, that's equal to 4 frames at 120fps, and it feels just as bad. However, because frames last a shorter amount of time at 120fps, a 1 frame dip isn't going to be as noticeable as a 1 frame dip at 60fps.
If the game is stable, and your monitor can actually display 120fps, then 60 FPS is never advantageous over 120. I play my gamesa t 165fps, and I only turn it down when I'm multi-tasking, or if my PC can't run that frame-rate while doing other things, like streaming, or something. So, I'll instead play at 90fps. Anything over 60, as I only play 60fps, when games are hard-locked to 60FPS.
Stable framerates are ALWAYS better, though. I'll take 30fps over 60 with dips into 40.