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Pros
Pro Contains many color-schemes
Pro Out of the box support for many applications (vim, terminals, etc...)
Base16 template repositories on github have configurations for most popular applications where a color scheme can be applied. This reduces headache for users when applying or switching color schemes.
Pro Its Solarized Dark scheme is compatible with htop
This is just one example of an app that doesn't work with vanilla Solarized Dark (half of the usernames in htop have the same color as the background)
One has to use a patched htop version.
Cons
Con Schemes are limited to 16 colors
You may not be able to use as many colors as you want for a particular application without manual manipulation since base 16 color schemes are limited to 16 colors.
Con Each theme needs manual tweaking
The base16 color schemes are really great but as a vim theme they require a lot of manual tweaking to be viable. One example is that in one theme a neon green bg is used with a white fd rendering any part of the vim UI that uses those two colors together illegible.