When comparing Cortana vs Process Hacker, the Slant community recommends Process Hacker for most people. In the question“What are the best power user tools for Windows?” Process Hacker is ranked 9th while Cortana is ranked 74th.
Ranked in these QuestionsQuestion Ranking
Pros
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 See programs with active network connections

Pro Real-time information on disk access
Pro 10x more detail and information about usage of PC resources and processes
Pro Can be set as your default task manager

Pro Detailed overview of system activity with highlighting

Pro Can create, edit and control services

Pro Can track which processes are using a file

Pro Open source
You can find the code here.

Pro View detailed stack traces with kernel-mode
Supports WOW64 and .NET.

Pro Graphs and statistics to quickly track down resource hogs and runaway processes
Cons
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 It might be a little intimidating for some users
