I seems to me that philosophy of Arch Linux is similar to OpenBSD in many ways. I have not used Arch to a large extent so these thoughts is mostly based on available documentation.
If I would need to go to Linux for some reason I would really check out Arch first.
Similarities
Minimalistic base installs
Similar package system with support for both precompiled packages and compilation from source. Good dependency handling.
Package installs does not activate/configure services automatically. A “user-centric” “do-it-yourself” approach is used.
OS and service configuration is performed in /etc/rc.conf. OpenBSD have moved some configuration to separate files e.g. for network configuration. FreeBSD still keeps most configuration in /etc/rc.conf.
BSD style rc.d based init are used.
Rolling release schedule similar to “following current” on OpenBSD. OpenBSD does however create releases (with extended testing and support) twice yearly which are recommended for most users.
Focus on great documentation. OpenBSD man pages are probably a few notches better than Arch.
Simplicity of functionality and implementation and minimalism.
Flexibility. Because all services are configured explicitly by the user the system may be configured with much freedom. For instance neither OS provide a default window manager.
Differences
Completely different kernel and legacy. Arch is based on Linux kernel and OpenBSD is based on BSD 4.4 architecture.
OpenBSD support many hardware architectures while Arch mainly focus on i686 and x86-64.
Arch support a larger number (30000 vs 6000) of packages.
Arch aim to deliver bleeding edge version of software packages. OpenBSD has higher focus on reliability.