Cask extends Homebrew by adding management of graphical applications.
SpecsUpdate
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Pros
Pro Extends Homebrew
Homebrew Cask adds functionality to Homebrew such as allowing downloads of commercial licensed apps.
Pro "Zap" application configuration
this is an interesting feature allowing user to remove application configuration leftowers
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.
E.g. brew cask install google-chrome
Cons
Con Cask update is usually manual
This defeats the purpose of the packet manager.
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.
Con Software no longer needed by anything (orphans) is hard to delete
Con The developers are hostile to the users reporting issues
Con Silently spies on the user by default
See here.
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.