GitExtensions vs Intellij IDEA

It's totally free
And its written and thought by developers who really know what you need as a developer. Open to contributions by everybody.

GitExtensions typically displays all commands that it carries out in a separate window. The user can also open the Gitcommand log (under Tools) and view the git commands as they interact with the program.

Instead of using HTTPS and authenticating every time they are pushing their code remotely, plenty of developers prefer to use SSH to communicate with the remote server and authenticate using secure key pairs.

Staging/unstaging files and/or lines of code, ammending, overriding commit's author, commit templates.

Complex git commands such as resolving a rebase conflict or performing a subtree merge are made much easier by a helpful UI.

GitExtensions has a simple layout, all usual functions being available without navigation menus. The branching and merging are clear and easy to follow.

GitExtensions is a lightweight and fast application.

Easy to save, view & pop stashes.

Can either be set up as a shell extension, standalone tool of Visual Studio plugin, allowing developers to choose the way that suits their workflow best and is easier for them to get into.

Can be used as a Visual Studio plugin for developers who use it as their IDE, or as a standalone tool. Both are easy to use even for users not very familiar with git.

Powerful submodule support, also when working with multiple cloned SuperRepos.

Includes Gitflow, also has a delete obsolete branches feature which is very useful to get rid of those old branches that have already been merged. There are also other options to clean overall clutter in repositories.

This makes running custom git commands quicker.

The settings window on first run helps you set lots of required settings such as your commit email address.

Makes working with repos using different languages and support tools much easier.

There are several out-of-the-box plugins installed with standard setup. Additional behavior customization is possible with new plugins (written in C#).

There is a free community edition (open source) and an ultimate edition, which you can compare here.

The ultimate edition is available for free for one year for students but must be registered through an .edu e-mail account.

Uses a fast indexing technique to provide contextual hints (auto-completion, available object members, import suggestions).
On-the-fly code analysis to detect errors and propose refactorization.

IDEA has a clean, intuitive interface with some customization available (such as the Darcula theme).

IntelliJ IDEA hardly ever crashes or has any issues that plague other Java IDEs like file corruption or slowness.

IntelliJ supports many languages besides Java, some of these are: golang, Scala, Clojure, Groovy, Bash, etc...

IDEA places an emphasis in safe refactoring, offering a variety of features to make this possible for a variety of languages.
These features include safe delete, type migration and replacing method code duplicates.

Many plugins are available for almost any task a developer may need to cover. Plugins are developed by Jetbrains themselves or by 3rd parties through the SDK available for writing them.

A very complete development environment support.

The documentation is exhaustive, easy to navigate, and clearly worded.

With ability to step into a certain part of a large method invocation (Shift+F7), drop frame, executing code snippets, showing method return values, etc.

These simplify the daily work, e.g. copy/cut a whole line without the need to select it.