In what scenarios does one have to run privileged LXC 1.x containers

We have a requirement to replace Solaris zones with Linux containers, that's why we are evaluating LXC1 containers. Since it's not safe to run privileged containers, can anyone shed some light as to when it's necessary to run containers in privileged mode? As running them in unprivileged mode would require a lot of tinkering with scarcely documented CAPs (Linux capabilities) apparmor/ selinux contexts, cgroup controls (depending on unique requirements in each application's case)?