Here is a comparison of HPCS Singularity vs NeRSC Shifter. They both bring the benefits of container to the HPC world. As such, both provide very similar features. The subtleties are in their implementation approach. MPI maybe the place with the biggest difference.
HPC workflow doesn’t benefit much from process isolation, thus by default share most everything, so process running inside container is largely the same as running on actual host. But process namespace isolation can easily be enabled.