OBS and your game are sharing the GPU.
While OBS is running, every frame the game renders is an opportunity for OBS to render a frame.
OBS renders its own frames (because it's a compositor, not a recorder) and does so constantly while it is open, whether or not it is recording or streaming.
In addition to rendering its internal frame for recording or streaming, if the preview window is on, it's rendering the preview-- and if studio mode is on, it's rendering both Program and Preview windows as well.
OBS renders those windows at the refresh rate of the monitor-- meaning even if you've set OBS to record at 60fps, its internal frames are rendering at that rate, but the preview and program windows are rendering at your refresh rate.
So if you're trying to do a 30fps capture of a 60fps game (let's say you're capping your framerate, or have vsync on) then if everything goes as expected, OBS' job is pretty simple-- take every other frame the game renders, and render it. Boom, you now have a 30fps capture of a 60fps source. It's less smooth, but as long as none of the frames are late and the GPU isn't overloaded, it's as good as a 30fps version of a 60fps thing can be, and all it has to do was sample 60 down to 30 by taking every other frame.
Now you want to do a 60fps capture of a 144hz source. Every other frame of 144hz is 72. So you now need to fit 72 frames of motion into a second in which you're only allowed to render 60 frames. 12 frames need to be dropped. But which 12? There's no method of doing so that does not result in the gaps between some of your frames covering more time than others, which means judder/stuttering.
Bottom line: You're either prioritizing your own viewing experience, or your audience. Even the most powerful cards currently available are not fully able to render some of the latest games at full quality on a high refresh rate monitor AND also capture, render and encode 1080p60 without lag, and even if they were, you would STILL have some lack of smoothness caused by the translation of 144 down to 60.
Prioritizing the audience experience, for the vast majority of situations, means either running applications at the same framerate you're broadcasting at (60) or at least at a refresh rate that is compatible with a simple sampling down to that framerate (120).
If you're encountering a specific performance issue please post a log and I can see what it says about your problem.
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