OpenVZ vs KVM

OpenVZ and KVM are two very different virtualization technologies. OpenVZ is OS level virtualization, which is extremely fast, but offers less customisation options (e.g. an OpenVZ VPS cannot run custom kernels, non-standard kernel modules or non-linux Operating systems). For most people, this limitation does not affect them. KVM is "Full Virtualization"; where each VPS runs its own kernel independent of the host. This allows significantly increased support for applications that interact heavily with the kernel; along with custom kernels and non-Linux operating systems.

OpenVZ KVM
Price Cheap Cheap
Upgradable Yes Yes
Downgradable Yes No
Custom kernel/any OS No Yes
Docker Support No Yes
Encrypted Filesystem (FDE) Support No Yes
Emergency access Yes, VPS must be booted Yes - Access to bootloader and console
L2TP/IPSec Difficult Yes
One-click Install Yes Optional
PPP/PPTP Yes Yes
Selinux supported No Yes
Speed Fastest Fast
TUN/TAP Yes Yes
SSD Cached OpenVZ VPS SSD Cached KVM VPS

Which should I choose?

In 2018, generally KVM is the better choice. The only situation where OpenVZ would be a better choice is if you need a really lightweight system with little to no overhead -- in terms of functionality and cost; KVM wins.