KVM and XEN are forms of full virtualization which have access to their own kernel instead of sharing the kernel with the node. OpenVZ is not full virtualization, it is more of an over glorified jailed environment that has the ability to limit your resource usage and give you root level access to your jailed environment. KVM is full virtualization which means you can actually choose your own kernel to run. Xen-HVM is almost the same as KVM as you can choose your own kernel to run, but depending on the configuration you can get better performance out of KVM than Xen-HVM. There is also Xen-PV which is still Xen but you use a pre-selected kernel for your instance which you can't directly change (it is part of the template you choose). You still enjoy the full separation of your resources and the ability to use your own kernel modules, however you can not change the kernel that is in use. For users wishing to setup drive encryption or use kernel modules which are not usually provided in OpenVZ (NFS, FUSE, ipcontrack,etc) XEN/KVM options will allow you to also load your own kernel modules. A lot of the modules are usually not available on OpenVZ because of the shared kernel and potential for it to cause issues for other customer. In OpenVZ you have no file privacy (beyond trusting the node operator) as you share your data storage space (usually on a single partition) with all other users. The node operator is able to see all your files without even entering your instance, as all you files are stored in your directory under the storage volume and can be seen from the node. It is still possible under Xen-pv for the node operator to see your data if they enter your server or mount your drive partition outside your server. KVM/Xen-HVM this is true as far as being able to mount your drive outside the instance, however, when you install your instance, if you install an distribution that supports it, you can encrypt your whole drive making it so without the key your data can not be seen..
There are other things as well, but these are the biggest of them. I hope this helps.
Cheers!