Your question really doesn't make much sense. "Linux" is not an operating system (before giving me a thumbs down actually take the 30 seconds to google it), it is a KERNEL. That said, if I am interpreting this question correct, as "What is the best operating system that uses the linux kernel", I would have to respond by saying that there is no correct answer to the question. Each linux disto has it's advantages and downfalls. Unless you need something really specific, such as, update repositories that update their software with cutting/bleeding edge packages, pre-compiled binaries (CERTAIN ONES), you write software for a carrer, or a really good community to go to for help, it comes down to personal preference.
Most linux distro websites usually have a type of "who this linux distro" is for page/forum sticky to help you decide if their distro is for you. For example, my favorate distro (archlinux) lists this on it's wiki.
" Arch vs LFS
LFS, or Linux From Scratch, is just that; the minimal base package set for a functional GNU/Linux system, manually compiled and configured from scratch. LFS is as minimal as it gets, and offers an excellent and educational process of building a base system. Arch provides these very same packages, plus a BSD-style init, a few extra tools and the powerful pacman package manager as its base system, already compiled for i686/x86-64. LFS provides no online repositories; sources are manually obtained, compiled and installed with make. (Several manual methods of package management exist, and are mentioned in LFS Hints) Along with the minimal Arch base system, the Arch community and devs provide and maintain many thousands of binary packages installable via pacman as well as PKGBUILD build scripts for use with ABS- the Arch (source) Build System. Arch also includes the makepkg tool for expediently building or customizing .pkg.tar.gz packages, readily installable by pacman. Judd Vinet built Arch from scratch, and then wrote pacman in C. Historically, Arch was sometimes, therefore, humorously described simply as "Linux, with a nice package manager."
Arch vs CRUX
* Q: Is Arch Based on CRUX?
* A: No. Arch is independently developed, was built from scratch and is not based on any other GNU/Linux distribution.
Before creating Arch, Judd Vinet admired and used CRUX, a minimalist distro created by Per Lidén. Originally inspired by ideas in common with CRUX, Arch was built from scratch, and pacman was then coded in C. The 2 share some guiding principles; for instance, both are architecture optimized, minimalist and K.I.S.S. Both ship with ports-like systems, use *BSD-style init systems and, like *BSD, both provide a minimal base environment to build upon. Arch features pacman, which handles binary system package management and works seamlessly with ABS, the Arch ports-like system. CRUX uses a community contributed system called prt-get, which, in combination with its own ports system, handles dependency resolution, but builds all packages from source, (though the CRUX base installation is i686 binary). Arch officially supports x86-64 and i686, whereas CRUX is i686 only. Arch is a rolling release and features a large array of binary package repositories as well as the AUR. CRUX provides a more slimmed-down officially supported ports system in addition to a modest community repo.
Arch vs Slackware
The mighty Slackware and Arch are quite similar in that both are simple distributions focused on elegance and minimalism. Slackware is famous for its lack of branding and completely vanilla packages, from the kernel up. Arch typically applies patching only to avoid severe breakage and preserve functionality, if absolutely necessary. Both use BSD-style init scripts. Arch supplies a package management system in pacman which, unlike Slackware's standard tools, offers automatic dependency resolution and allows for more automated system upgrades. Slackware users typically prefer their method of manual dependency resolution, citing the level of system control it grants them. Arch is a rolling-release system. Slackware is seen as more conservative in its release cycle, preferring proven stable packages. Arch is more 'bleeding edge' in this respect. Arch offers ABS, an actual ports-like system. The (unofficial) Slackbuild system is very similar to Arch's AUR concept. Slack users will generally be quite comfortable with most aspects of Arch. "