Chakra's internals are pretty similar to Arch's, since Chakra was derived from it. Also, right now both share pacman and makepkg as the package management system. But Chakra gets more different from Arch every day.
Chakra's installation media is really easier than Arch Linux. It runs and installs the KDE Desktop from the beginning and installs many applications by default, as opposed to Arch. Also, Chakra includes a community repository, which is designed to install applications which would not fit the repos, and it can be compared to Arch Linux AUR.
Chakra packages are normally more stable than Arch ones, but Arch has many more applications than Chakra, and that without counting the AUR.
For more detailed information about the differences between Arch and Chakra, please see the FAQ. Be sure to reference it early and often as you learn more about the Chakra philosophy and systems, particularly package management.