Debian is composed of free software mostly carrying the GNU General Public License. The operating system is developed by an internet collaboration of volunteers aligned with The Debian Project.
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Pro Wide choice in desktop environments
Debian offers stable and testing CD images specifically built for GNOME (the default), KDE Plasma Workspaces, Xfce and LXDE. Less common window managers such as Enlightenment, Openbox, Fluxbox, GNUstep, IceWM, Window Maker and others can also be installed.
Pro Very stable
Debian has a Stable branch, where packages are thoroughly tested before release. Furthermore Debian is know to be the definition of stable when it comes to production systems.
Pro Wide choice of hardware platforms
Debian has the widest choice of hardware platforms, including:
amd64, armel, armhf, i386, ia64, kfreebsd-i386, kfreebsd-amd64, mips, mipsel, powerpc, sparc, s390, s390x, source, multi-arch.
Pro Standard vanilla Linux desktop
Debian runs standard Gnome, XFCE, KDE - it doesn't use its own special desktop environment or debian specific modifications or customisations, which means that users benefit from the work of the whole Linux community, Debian developers can focus on the distribution itself, and any support for your desktop environment on other distributions should work on Debian as well.
Pro Install and forget
Once installed you can almost forget about it and start to use your desktop for your daily tasks.
Pro Easy to find help with any problem
Debian is one of the oldest and most popular distros out there. Debian's popularity means that you will always be able to find a solution for your problem just by searching on Google, or if by chance nobody has had the problem you are having it's very easy to ask the community and quickly get a solution.
Pro Comes with over 55.500 packages
Because of its popularity, Debian has a lot of applications available which range from productivity programs to business software, games and development tools. It comes with over 55.500 packages (software that is precompiled and ready to be installed on a local machine) -- all of them for free.
Pro Highly secure system
Known for being consistent in maintaining a highly secure system. Several other popular distros use Debian as a base or core for their own Linux OS, the security being one of the main factors why it's so commonly used.
Pro Rolling or Release based
Every Debian Release can either use a Rolling or Release based model.
Pro Well-working team
The developer works very well so the the code is one of the best written out there.
Pro Live install images for CDs, DVDs and USB thumb drives
Debian releases live install images for CDs, DVDs and USB thumb drives, for the i386 and amd64 architectures, and with a choice of desktop environments. These Debian Live images allow the user to boot from a removable media and run Debian without affecting the contents of their computer.
Pro Big open-source project
The Debian project is one of the biggest open source projects with over 5000 active contributors.
Pro A lot of ways to install software
You can either use aptitude, apt or apt-build to install software from the Debian package archives.
Pro Great for gaming
As Debian is the base for SteamOS and because Ubuntu is based on it, it's almost certain that all Linux games will run properly and require no hacks like creating symbolic links because of some hardcoded paths.
Pro Supports SecureBoot
You don't have to disable SecureBoot if you use it, which is useful for LiveUSB or dualboot setups.
Pro A real installer
Unlike other distributions that just extract their Live image, Debian offers a real traditional and modular installer to customize the installation.
Pro The Debian Social Contract
Guaranteed commitment to adherence to values, principles, priorities, requirements and guidelines by the Debian project.
Pro Strict seperation of non-free software
Debian is one of the few distros that let the user choose if he wants a free system or not.
Depending how it is configured debconf does the most of the hard work for you and only asks you with configuration /file conflicts.
Pro Many ports
Debian supports almost any Kernel maintained CPU instructions set. It has also a few non Linux Ports.
Pro Widely supported
Almost any software that is available for Linux provides a Debian package.
It is possible to rebuild the entire system and optimize it for your hardware (of course, it is not as detailed as Gentoo's USE flags).
Pro Unique release cycle
The most Linux distros have one or two stages before a release, but Debian has five before a new stable version is released (experimental > unstable > testing > code-freeze/bug hunting > stable).
Pro TUI installer
The Debian installer can still be launched as text/curses-like installer which is more compatible and keyboard-friendly than the graphical version.
Pro Standard archives
Debs are normal ar and tar archives with shell scripting and additional gz, bz, lzma or xz compression.
Pro Great choice for returning Linux users
If you haven't use Linux for a long time, say 5-10 years, it's a great distro in which you can quickly get in the boat again. You don't have to worry about falling back. Everything is in its place.
Pro Has small amount of today's bugs (e.g. no duplicate web cameras in Skype - likely not Skype's fault)
But has quite a few bugs from 2016-2017, apparently for long term.
Pro Inconsistent init systems
While Linux uses systemd, non-Linux ports use the traditional sysvinit.
Con Stable release contains extremely outdated packages
If you want the newest packages, you'll have to do a minimal installation of Debian stable then upgrade to testing or you need to install testing directly: https://wiki.debian.org/DebianTesting.
Con Internal quarrels harm the project
Instead of working all together to provide the best Operating System, some maintainers are just ignorant and aggressive to new ideas or new maintainers. That led to many crises and controversy in Debian's history.
Con Ridiculous package splitting
Even though it makes sense to split devel and the actual binary of an application, the splitting has become as mess in debian and its derivates: for example the nvidia driver is splitted into over 40 different packages: https://packages.debian.org/en/source/sid/nvidia-graphics-drivers
Con No choices
Debian basically doesn't give you any choices, even dpkg supports this feature with virtual packages: for example, it is very hard to use a different sound system than ALSA, like OSS4 or to use ALSA with pulse audio emulation, and the same goes for different init systems.
Con No default support for unfree drivers
Debian does not official support unfree software so if you have a wifi card or anything elese that requires an unfree driver you will need to download the unofficial/non-advertised non-free iso image which contains all unfree driver packages.
Con Not designed for general desktop usage
By default, Debian Stable is not that great of a distro for general desktop usage, since the packages are very outdated. You'll have to spend a while configuring the system in order to make it work.
Con Outdated kernel of the live system
Since the LiveCD is based on Debian stable the kernel is old, outdated but stable.
Con Breaks if you suspend/resume
Breaks when you resume the activity on the system if you use nvidia cards.
Con Buggy and non-user friendly
You need to know almost as much as Arch and deal with documentation not as good as the Arch wiki in order for Debian to work.
Con No good choices of fresh desktop environments
GNOME is quite outdated and buggy;
KDE is too old, even in Sid it is at 5.14 branch (at Jun 13 2019 Plasma 5.16 is available in many rolling/fresh distros);
XFCE behaves like crooked, visual artifacts at the taskbar and so on;
Cinnamon as far as I know works better in Linux Mint compared to (almost) any other distro;
For other desktop environments (e.g. MATE) can't say - these are too new (as projects) and possibly incomplete, thus might have many bugs.
Con Hard to learn
Con Old software is not useful, but is stable
Certainly for the stable and old stable versions. But the testing version has quite up to date software.