You're on a OpenVZ VPS so you can't update the kernel which is one of the downfalls of container VPS such as OpenVZ, LXC etc - The kernel is managed by the hosting provider and its up to them to update it. You also can't run a custom kernel.
If you want management over your own kernel or want to run a custom kernel you need to look at a full virtualization VPS that uses either KVM or Xen for example.
So - the only difference between OpenVZ and e.g. KVM is:
1. OpenVZ allows only OS-level virtualization and does not allow its users to modify the kernels.
2. KVM provides kernel-level virtualization with each virtual level having its own RAM, kernel, a network card, graphics adapter etc.
But regarding "kernel" and OS SECURITY are both vulnerable and no one is "more" secure then the another.
If you are pin pointing to the feature of each technologies one by one in all the technical aspects, yes there are lot more which some one who need to glance before they are going to adapt any one of these technologies for their business purpose.
KVM and OpenVZ are mature technologies, user space applications in Linux like LAMP stack webhosting or intend to have better performance with limited disk and memory foot print then OpenVZ is the choice.
One of the features to run different Operating systems apart from Linux then KVM is a solution, which provides better reliability and stability.