Cask extends Homebrew by adding management of graphical applications.
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Pro Extends Homebrew
Homebrew Cask adds functionality to Homebrew such as allowing downloads of commercial licensed apps.
Pro Manage graphical applications through the command line
Homebrew Cask allows you to install graphical applications through the command line, rather than having to go through the standard installation process.
brew cask install google-chrome
Con Duplicate apps found in brew may cause issue
There are warnings provided that apps found in brew should not be installed with brew cask (and vice versa). While the user is warned of this, mistakes can happen, which would be better to just see them avoided all together by not supplying duplicate apps.
Con Requires Xcode
Homebrew Cask requires that Xcode is installed, which may be more work than what some want to spend on configuring this app.