if you want things to be smoother than 60hz, then yes you need a 120/144 (i have 120hz)
but, your rig should be able to push past 60fps, close to 100 and you should be able to notice the difference.
another option is to lower the settings. what i do in bf3 bf4, is to use medium settings so i could hit above 100fps. i just trade eye candies for the extra fps. medium is not bad anyway (for that game) and once you are playing, you don't really notice how shiny the floor is in the middle of the fire fight