Hey guys,
I'm not entirely sure if i'm having the same problem, but i've managed to (somewhat) fix mine so i'm posting the whole story here just to see if it helps somebody (if it doesn't, i'm sorry and i wish you good luck).
So, just to make sure it isn't a problem with your game, Windows 10 has problems with Game mode and running games in borderless window mode specifically. For me, Path of Exile wouldn't go above 30 fps and frequently dropped below 30 on a 1070 GTX. To fix that, press windows key + G to bring up the game bar, and select the button furthest to the right to turn it off. Haven't had a problem since with borderless window in months.
Assuming it's not that, i ran into another issue tonight involving Streamlabs OBS (which i imagine is similar to normal OBS).
While streaming, i added a Display Capture source to my main Live scene to show my 2nd monitor on stream. In that same scene, i already import another scene called Game Cap where i have a Display Capture source, showing my 1st monitor. Afterwards i removed the 2nd display monitor capture.
After this the FPS in SOBS *tanked*, while being fixed at 60 FPS for months before. Everytime i would go back to Overwatch (the game i was streaming at the time) the FPS in SOBS would drop around 20-30 FPS. My ingame FPS where fine, and stayed as high as they ever where. Neither am i dropping frames, haven't dropped a single frame all night.
Now i've found several things that affected this problem. At first my ingame FPS were between 80 and 106, since i set the limit to 120 which i never get. Once i capped it at 60, SOBS stayed at a solid 60 too, making me think it was a resource allocation problem, but now i think that is not the case.
Changing stuff around, i found that when i changed the source in my game cap scene from a Display Capture to a Game Capture source, the problem cleared right up. Even unlocking the FPS on the training course in Overwatch i can shoot like a madman, bouncing the ingame FPS between 80 and 100, while doing nothing to SOBS - solid 60 FPS. Regardless of whether OW is set to Borderless Window or Fullscreen.
Similairly, i've found that running the game in Full Screen mode, where by default i have it in Borderless Window mode, makes the FPS go back up to 60 in SOBS as well, regardless if i'm using a Game Capture or a Display Capture. Again, i can do whatever i want, solid 60 FPS on stream.
Really, the problem only happens if i'm streaming Overwatch in Borderless Window AND i've got my SOBS set to Display Capture (i have not checked for problems in other games), which started after i added a 2nd Display Capture source to my live scene on stream. Restarting the stream or rebooting my PC hasn't worked, neither has deleting/remaking display capture scenes. Which made me think of windows game mode, as mentioned in the beginning, but i checked and it is still turned off while the problem occurs.
This all makes me think it's some kind of bug with multiple display captures within the same scene. I'm no programmer, so i wouldn't know - also i've been drinking somewhat tonight :p I'm just relaying what caused a (similar?) problem and what, for now, fixed the problem for me.
Again i can only reply to the first poster since i encountered an issue where the FPS in my OBS would drop, where previously it was fine, seemingly without cause. And i'm not downgrading my entire system to windows 7 for this :p For others with similar but different issues, best of luck :) As for my issue, a fix would be nice since changing the game being captured for every game or running everything in Fullscreen while alt-tabbing is a pain :p
Finally my system specs:
Intel Core I7 6700k
64GB ram
Nvidia 1070 GTX (driver 416.94 atm)
Windows 10 Updated to whatever the hell is the current update
No Gsync or Freesync monitors (so that isn't the issue).
For live footage about the problem i've streamed the whole thing tonight (5/12/2018) which'll be available for 2 more weeks till my non-affiliate status kills the vods :p Twitch.tv/desogames
I hope i've been of some help,
Deso.