Is all your monitors 120 Hz or is all your monitors 60 Hz?
Using fullscreen and not windowed borderless?
Windows Aero/DWM have some problems with mixing different refresh rates and forced v-sync in multiple monitors. It may slow down both displays to v-sync a slower 60 Hz monitor, expecially in game's windowed or borderless mode.
For windows 7, turn off Aero. But, windows 8 and 10 can't easily turn off Aero/DWM if at all, as says in the log file. If only there was a way to turn off Aero/DWM's v-sync that I don't know how yet...
This problem is mostly not limited to OBS, I also have some frame rate jitter problems when using 2 monitors like playing a YouTube video or animated GIF on one monitor and playing game on the other monitor in windowed mode. Problem don't show up on windows 7 while Aero is off.
I have 4:3 CRT monitor at 1280x720 115 Hz or 1280x960 85Hz, and 2x LCD 1920x1080 60 Hz.
https://www.google.com/search?q=poor+dwm+performance+multi+monitor+mixed+refresh+rate