I'm kind of getting the same issue as you guys. When I play Diablo 3 everything it is perfect when I stream/record but when I play Final Fantasy 14 online everything hits the fan. I checked to see if it was my internet connection and no that wasn't it I reinstalled OBS Studio to see if that would fix it...and no again. It doesn't affect my gameplay at all everything there is perfectly fine there but when I look over on my second screen where OBS is at with Studio mode the right hand screen mirror is lagging and that is what is being recorded or even streamed. But I will tell you of what I found out that helps which still confuses me when I know Diablo works fine even with a overclocked monitor. When playing FFXIV I can't overclock my monitor which I'm fine with because it automatically does that with some games I play, but what I have found out by lowering my graphics setting within the game helps OBS a lot. But this brings another question, why does it work fine in some programs/games when it does not in others? Oh not to forget, this will help with those that have Nvidia Graphics Cards...SLI, when you connect them with the Nvidia Control Panel make sure you set the Physx settings to the card you want to use for the Physx and dedicate it, that will be a huge help in that as well.
But if you want to know my specs here they are...just to forewarn you I'm really good with computers and know what I am doing with them.
CPU/Processor: AMD FX-8370 (Eight-Core)
Motherboard: Asus Sabertooth 990FX R3.0
Memory/RAM: G.SKILL Ripjaws X series DDR3 SDRAM 2400
Graphics Card: 2 Nvidia Geforce GTX 960 (SLI'ed together)
I don't remember the hard drive model that I have but it is a SSD Samsung.
Oh if you are using the Nvidia Graphics cards make sure that you also have your settings in OBS Studio
set the encoder under output to Hardware. That will use your Graphics card for the record/stream instead of your CPU.