Do you get the same difference if you compare them on the *same* monitor? Cheaper screens can have some variance, both from one serial number to another, and with different viewing angles.
If you eliminate that, and you still have a difference, then you might look at this setting in the source properties:
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and this in OBS settings:
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The Limited range is a holdover from analog TV broadcasts, where nothing is ever equal, and the broadcasters wanted to make sure that full-white and full-black were actually displayed that way. So they overdrove it slightly. When digitizing those signals, it was important to keep the full transmitted (overdriven) range, so that playing back the digital version on an analog set still produced the same result.
With the *entire* signal path being digital now, that's not a technical problem anymore. Only a legacy one that can't seem to die yet. Sending one setting to something that expects the other, will result in it being slightly washed out, or slightly too vibrant, depending on which direction the mismatch goes.