Xen VPS's are more closely related to a dedicated server as they are paravirtualized. This gives you full customization of your server, including custom kernels, root access, installation of programs and services, rebooting of the virtual environment and reinstallation of the operating system. Xen also offers more flexibility for the type of operating system you can chose from such as Windows, Linux, Solaris and BSD.
OpenVZ VPS's are virtualized and run off a single kernel. They allow for all the same functionality as a dedicated server with features such as root access, multiple IP's, installation of programs and services, rebooting of the virtual machine and reinstallation of the operation system. OpenVZ VPS's do not offer the full functionality when it comes to customizing the kernel as every VPS is run off a single kernel from the host node.