When comparing Slackware vs Slax, the Slant community recommends Slackware for most people. In the question“What are the best Linux distributions for desktops?” Slackware is ranked 5th while Slax is ranked 54th. The most important reason people chose Slackware is:
Uses stable, plain-vanilla packages from upstream.
Specs
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Pros

Pro Stable
Uses stable, plain-vanilla packages from upstream.
Pro Strong adherence to UNIX Principals
Pro Ideal to learn more of Linux
Follows the original Linux roots. It still sees Linux as a free clone of UNIX so the distribution tries to be UNIX-like.

Pro Package management
Uses standard tar archives with shell scripting as packages.
Pro One more distro which is init based
Some users don't like to install systemd based distros because they increase booting and processing speed.
Pro Oldest surviving Linux distro
Besides Debian (which was first released in August 1993), it is the oldest still maintained Linux Distribution and was first released in July 1993.
Pro Super fast
Pro No systemd
Pro Persistent changes
Changes you make in the configuration persist if you run from USB.
Pro Pretty fast to boot up
It was considerably fast to turn on when booting from cd.

Pro Modules
Standard tar archives plus some simple shell scripting produces modules that you can load dynamically into the OS for added apps and functionality.
Pro Modern desktop

Pro Small footprint
About 200mb, but with a full KDE4 environment and loads of useful apps.
Cons
Con Not user-friendly
It is made to be KISS (keep it simple, stupid), so you have to do everything by hand.
Con Large size live ISO
One needs to vain 3GB+ data for downloading one slackware ISO.
Con Narrow repos
Doesn't offer the same amount of options as other distros do.
Con Niche/small community
Slackware is its own niche and has a small community.
Con Very slow release cycle
Hasn't updated in 3+ years.
Con Dependency issues
When it comes to dependencies, Slackware shows more issues than many other distros.
Con Overly complicated HDD/SSD installation
While it has a nice layout Slax's lack of an installer tool like Tinycore's just can't be justified. It seems strange that it comes built in with programs that some users may not want, yet it doesn't have an easy way to install it. Due to its heavier use of RAM, built in software, and lack of an installer its hard to choose it over TC.
Con Works slowly on old computers
Con Infrequent releases
Since Slax is maintained by only one person, releases are not that frequent. So it may take a while to get bug fixes or new features once you start using it.
