When comparing Cortana vs Cygwin, the Slant community recommends Cygwin for most people. In the question“What are the best power user tools for Windows?” Cygwin is ranked 20th while Cortana is ranked 47th.
Ranked in these QuestionsQuestion Ranking
Pro Can recognize music
You can ask Cortana what music is playing and she will attempt to identify it.
Pro Will let you know when artists you're interested in play in your area
Cortana monitors your Bing search history, social network actions, music played, etc to find out what are your favorite artists and will let you know if they plan to play in your area.
Pro Additional packages available via Cygwin Ports project
Pro Better default terminal
Cygwin's default terminal "Mintty" is far better than CMD.
Pro You can run graphical applications
It has X Server.
Con Functionality is limited on non-Windows devices
While Cortana is available on Android and iOS, certain features on those operating systems are either limited or non-existant. For example, there's no hands-free voice activation on iOS, and on Android it's only available on the homescreen and nowhere else, etc.
Con Many incompatibilities
A lot of tools don't actually work with Cygwin, and documentation is often sparse, so for many use cases, it's worth the small bit of extra effort to just run a full virtual machine.