The ancestor of Docker at dotCloud ran on openvz. We moved to lxc in 2010 when it became usable.

I think of them as mostly interchangeable except for the shared hosting use case where openvz has a head start (more time for more eyeballs to audit and fix it).

Now the whole "openvz vs. lxc" distinction is pretty moot - linux has namespaces and cgroups. Everything else is a matter of choice of userland libraries and cli tools.