VPS (Virtual Private Servers) uses some Virtualization technologies, such as Xen, Virtuozzo, OpenVZ (free version of Virtuozzo), Virtualbox, KVM/Qemu, VMWare and Virtual Iron.
Linux has a lot of great VM options. VMware is a great free (cost) option, and KVM has become a great option very quickly. OpenVZ and VServer are interesting light weight OS "jail" virtualizations. They each have pros and cons, depending on your requirements and apps being used.
OpenVZ is somewhat like FreeBSD Jails. It provides some separation which makes it easier to manage multiple complex servers. For example, it makes sense to run a web server and mail server in two separate virtual machines, since it keeps the configuration independent.
Xen, is like VmWare or Qemu and provides an independent virtual machine for each system. These systems can be anything at all: Windows, Linux, BSD, whatever.
Performance wise, OpenVZ is bound to win, because it is a different solution to a different problem.
Xen is good when you want to run different kernels (different OSs).
OpenVZ, on the other hand, employs a single kernel model, which makes it suitable for you if you only want to run Linux (different distros are possible, different kernels are not). But in this very field OpenVZ is way better than Xen -- not only in terms of performance, but also scalability, manageability, density, and usability.
Speaking of isolation and security, OpenVZ runs on thousands of ISP/HSP servers, and everyone can buy a VE (Virtual Environment) for about 10-15 bucks a month. There one have a root account and can try to exploit the system in all the possible ways. So far those HSPs are not out of business yet, that practically proves the system is secure and properly isolated. More to say, security comes from the constant care, and we (OpenVZ team) do care for security a lot.