OpenVZ is container-based virtualization for Linux. OpenVZ creates multiple secure, isolated containers (otherwise known as VEs or VPSs) on a single physical server enabling better server utilization ... More
I played around with OpenVZ as well as Xen, to decide which one I would use for a virtualization project for my company. I ended up choosing Xen as the clear winner. There are some benchmarks out on the web which show OpenVZ has a very slight performance benefit over Xen. However, the performance benefit appears to be negligible in most circumstances, and I found Xen much more user friendly. Xen is much more manageable, and makes it easy to save a copy of a virtual machine. It also provides mechanisms for moving a virtual machine to another host running Xen in realtime, with the virtual machine taking a "hit" for only a few milliseconds. I did not test this functionality, but just illustrates how more mature the Xen project is over OpenVZ.
Having said that, OpenVZ does provide some things Xen does not provide. It allows "over subsubscribing" system resources such as memory, and allows more finely tuned tweaking than Xen provides. Also, if you are familiar with Zones in Solaris, you'll feel more at home with OpenVZ than with Xen.