[Unixfy]

As many others have pointed out already, the question can not really be answered. It depends on what you want to do.
If you just need process sepperation you should go with a container system like OpenVZ or any other, it is lighter you can (para)virtualize much more on the same hardware. It does not run its own kernel, it is basically just something like a jail for processes.
KVM on the other hand is different, it more or less simulates your own PC or Server inside your Sever, it runs it's on kernel which gives you the opportunity to install a totally different Operating System at the cost of resources.
It is like comparing a bike with a truck, more or less.
So it depends on your usecase, just want to run a webserver sepperated from your other applications, go with a container setup. Need to run another Operating System you have to go with full virtualisation.

Also older processors do not support full virtualisation at the cpu level, so your virtual machines will be slow, the only sensible thing there is to do a container setup.

No, OpenVZ is just an advanced chroot
It's not any lighter, it's just that resources are not dedicated so you can oversell. 
KVM doesn't technically run it's own kernel, it's just full virtualization not partial virtualization.

By the way, have you ever tried an OpenVZ container in a KVM VPS? It works

You are either misinformed or misread me or i did not make myself clear, or all of the above. It(container setups) is actually a lot lighter since it does not run its own kernel and does not have to virtualize devices as in simulate a whole server. Also it does not have to load drivers.

You can also oversell resources with kvm or vmware, it's pretty much the same thing. You are out of ram if you are out of ram, does not matter if you use the ram a container or a vm, you also don't have to dedicate all of the ram to a VM, there is also stuff like KSM. Same goes for disk space, there is thin provisioning but you only have so much diskspace available. If you are full, you are full, no matter if its from VMs or Containers.

And yes, you do have to technically run your own kernel in a KVM, otherwise you have no operating system.
Btw have you ever tried kvm in a kvm, it works.

In my past experience, I have nearly identical resource usage between OVZ and KVM (one VM of each, 512MB RAM, 1 dedicated CPU),  so....

You can oversell resources on KVM however when you try to use the VM it won't work. OVZ oversold VPSs will still work as not all resources are being used on the host.

I may have misread you about the kernel, I saw "KVM runs its own kernel" not "You run your own kernel".
When I tried KVM in KVM the host wouldn't start up again after it crashed