When comparing GitHub Desktop vs Fork, the Slant community recommends Fork for most people. In the question“What are the best Git clients for Windows?” Fork is ranked 2nd while GitHub Desktop is ranked 17th.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Great GitHub integration
This is the official GitHub desktop client built by the GitHub team.
Pro Simple, streamlined GUI
GitHub Desktop uses an extremely simplistic two-panel view. It's not capable of complex historical visualisations like other GUIs, but it is very easy to use (especially for git novices).
Pro Supports pull requests
In addition to being able to seamlessly and easily integrate with all of GitHub's features, it also supports forking and submitting pull requests on any open source project hosted on GitHub.
Pro Fast and easy to use
Pro Comfortable when staging line-by-line changes
This feature is superior to the one that is implemented by SourceTree as it does not reset the file scroll view to the top of the file after each stage.
If you do feature-specific commits after some time of development - it's very important to be able to easily compose the commit from different line-based changes.
Pro Smart Diff is very handy
Pro Tabbed interface
Several repos can be open at once in individual tabs, so it's trivial to switch back and forth between them.
Pro Overall aesthetic
The GUI components are flawless on the Mac. It is expected to be a similar experience on Windows. Once you realize that you can filter by branch, your appreciation for the product will go up dramatically.
Pro Dark theme support
Pro Highlights the difference within a line
Pro Merge Conflict Resolution is great
Pro Comfortable keyboard shortcuts
Pro Repositories with uncommitted changes have a * next to their name
This is an update from previous versions.
Cons
Con Limited
Can't handle complex tasks. The Help Manual advises to use command-line Git instead.
Con Does not support multiple Remotes for a repo
Only allowed to assign one URL as remote. To manage/sync/fetch other remotes, use command-line Git instead.
Con Overly Simplified UI
UI that is designed not to support the needs of power and enterprise users. Management of more than five repos is next to impossible.
Con Buggy
Poster child for authors' programming ideology (FRP), likely the cause for the odd quirks and bugs it has.

Con Not free/libre
This application is proprietary, and thus cannot be modified or freely distributed.
Con No Linux support
There's no Linux version of this client.
Con Non-GitHub repositories are not fully supported
Since this is mainly a GitHub client, other repositories are not fully supported and with as many features and setting up a repo hosted anywhere else but GitHub is troublesome.
Con Still a young client, thus not as feature rich
This git GUI client is quite young compared to industry old-timers like git-tower 2 or SourceTree. So it's not as feature rich as you'd like. Still a very capable client for a simple day-to-day work.
Con No Linux version
This git client is not compatible with Linux making the life harder for the developers that work on both, MacOS and some Linux distro.
Con Requires granting access to your git projects for the developer of the app
