When comparing gitk vs tig, the Slant community recommends tig for most people. In the question“What are the best Git clients for Windows?” tig is ranked 5th while gitk is ranked 26th. The most important reason people chose tig is:
If you prefer to do most of your development inside the terminal, changing windows to move to a GUI git client can be annoying. Since tig runs inside the terminal, that's avoided.
Specs
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Pros
Pro Visibly more compact overview output than many other options
When using gitk to scan a long list of changes, the user is able to see more of the list without pagination, as there is no huge buffer of whitespace between each entry.
Pro Fast
Since it's pretty minimalistic and does not contain a lot of features (for example, it can't commit), it's quite fast.
Pro Free
Gitk is a free and open source tool. It forms part of the official git suite.
Pro Comes with Git
Gitk is a part of the git package, so no additional application is necessary: it is developed right alongside git itself.
Pro Easy to use
Pro Allows you to stay in the terminal
If you prefer to do most of your development inside the terminal, changing windows to move to a GUI git client can be annoying. Since tig runs inside the terminal, that's avoided.
Pro Fast
Pro Vim-like bindings
Pro Available in Homebrew
Can easily be installed with homebrew simply by running brew install tig
Pro Works on any platform
Cons
Con Cannot commit
The user needs to use a different Git client (GUI or otherwise) to commit changes.
Con Does not automatically update
The user must press F5 to refresh the view as there is no automatic update available.
Con Steeper barrier to entry as compared to a GUI solution
Since you have to get used to working in the terminal (if you are not already used to doing that) and learn the commands, it has a steeper learning curve than GUI clients which are usually more intuitive and easier to grasp.