Both will run 1080p games really well, arguably overkill even. 5700 XT is somewhat faster, Nvidia comes with better software suite, most of which is of questionable importance for 1080p and 2060S. Namely DLSS and RTX - DLSS isn't needed and carries an image quality penalty at the resolution, and 2060S isn't beefy enough for ray tracing. RTX voice and Shadowplay might be useful for you, look them up. Radeon also has a capture feature, but it is basically only good for local recordings - low bitrate performance isn't good enough for streaming.
However depending on how patient you are, I'd wait for lower end offerings from both vendors, they're bound to offer better performance for the price. But I wouldn't expect them before February.
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i7 8700k - 16GB - 3080 XC3 Ultra - 660p 1TB + MX500 2TB - HE-4XX w/ Topping D30+A30
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