Parallels is the company responsible for the travesty of horrors that is Plesk.
The hosting company I work for (who shall remain nameless) uses OpenVZ for virtual servers. It is wholly inadequate and we have begun transitioning to KVM.
It's still trivial to forkbomb a container running the VZ kernel and take down the whole host. The container model also requires a number of really, really annoying limits (shared memory, locked memory, open files, total files, TCP sockets, total sockets, and on and on) that have to be there because of the fundamental weakness of the container model.
You can get around that by using a container just for one thing, but then you still have to have full operating system just for that one thing. If I want to have memcache by itself in a container, I need a full file system and Linux install to support it. You lose some overhead by using a container instead of a hypervisor, then get it all right back plus some with the requirements of containment.
The only advantage I can see is that you can update the hardware configuration in realtime. Other than that, use cgroups or use full virtualization.