I did a quick test, just to try to get an idea of what you are experiencing - and I have a similar GPU.
I use two 1440p monitors @ 144Hz. Both are DisplayPort. G-Sync disabled for this test.
RTX 2080 Super / i9 9900K (stock).
When I set "
Extend These Displays" in Win 10 and run Far Cry New Dawn built-in benchmark, showing in full-screen on monitor one, but the desktop is extended so the second screen is visible for other windows and tasks - but nothing running on hte second screen, i get
Min FPS : 89
Avg FPS : 114
Maximum FPS : 148
Frames Rendered : 7504
Screenshot : Extend These Displays - 1 Fullscreen and 1 idle screen
When I keep "
Extend These Displays" in Win 10 and run Far Cry New Dawn built-in benchmark, showing just on monitor one (still full-screen), but also running a full screen YouTube video on the second monitor, i get
Min FPS : 82
Avg FPS : 110
Maximum FPS : 140
Frames Rendered : 7200
Screenshot : Extend These Displays (two fullscreen apps : game & Youtube)
If choose "
Duplicate Displays" (the game showing on both monitors), and run the same benchmark I get
Min FPS : 89
Avg FPS : 114
Maximum FPS : 148
Frames Rendered : 7502
Screenshot : Duplicate Display (almost identical performance to the first test)
So the performance is not really severely impacted, by any of theese setups.
However -> I wanted to test with one screen at 144Hz and one at 60Hz, because I was under the impression that's how OP had the settings set.
But in my case, both monitors were forced to the same refresh rate (which seems to be determined by the lowest refresh rate - which makes sense), when I activated "
Duplicate Displays". I can use different refresh rates when extending displays.
So the only potential issue I can see with OPs setup is, that the main game is only displaying at a
60Hz refresh rate determined by the capture card, and if you are used to a higher refresh rate, the game would appear choppy if you are playing the game at just 60Hz - only if you are seeing a framerate above 60 FPS of course.
So I suspect that it is the
reduced refresh rate that gives the
impression of poor perfomance when duplicating displays, because as far a I can see, the potential peformance is pretty good despite running two different full screen application simultaniously (although just one actual game and one stream).
But I might have missed an obvious difference - I just ran three quick teests, and they are not very scientific, so to speak (and just one single game).
But it still makes me
suspect that the possible refresh rate descrease to 60Hz in Duplicate Displays-mode, caused by the max refresh rate of the capture card, is what's causing the issue.