100% depends on the vps. KVM and OPENVZ can both be oversold, and are mostly quite oversold on cpu-cycles, which is what you mostly need on a cod server.
HDD/SSD is not really an issue as you can tweak cod to only require IO when the map changes.
Mint is not an OS i'd consider for a server, as it is just ubuntu with a different GUI (and you will most likely not be using the GUI to begin with on a server). I personally prefer ubuntu over debian as I have run into issues with debian in the past. Centos also has some weird quirks regarding dependencies for libcod (especially the mysql client...)
And to return to the kvm vs openvz battle: at the same host, kvm is usually less oversold than openvz, but i've been running my cod2+4 servers off a dirt cheap openvz provider for a while without major issues. Currently running off a vmware virtualized host.