chemmajorp53 :
That's just so much graphics horsepower for such an outdated resolution when it comes to higher end hardware.
I'm not sure I would consider 1080p to be an "outdated resolution" when according to the current Steam Hardware Survey, only a little over 5% of Steam users have a 1440p or higher display. : P
That said, I agree that these cards would be overkill for a 1080p 60Hz panel, and you would want a high refresh rate screen (like 144Hz) if at that resolution, to pair with hardware like that. You mention it being a "secondary" screen, but what kind of screen are you intending to use with this system?
As for the question, obviously if the 2070 were just $10 more, it should be the better choice. The main issue with the 2070 is that it typically costs notably more than a 1080, for only marginally better performance and some new features that are not yet available. At roughly the same price, it's clearly the better option though, as it should be able to run raytraced lighting effects and DLSS antialiasing in certain games eventually, which the 1080 doesn't have the hardware for. As far as new graphics card launches go, the 20-series has been a bit underwhelming so far, especially after 2 1/2 years, but that's more down to the performance gains being minimal at an increased cost, with the new functionality still not available in any form.