With containers, both the kernel and the hypervisor are shared. With vms, only the hypervisor is shared.

It's a matter of having a smaller attack surface. There are plenty of container images that run with root access by default, which is almost full access to the kernel. This means that if the application running in the container is compromised, you need to rely on the kernel enforcing the sandbox between containers. This is a relatively new threat (root not being fully trusted), so beyond there simply being more attack surface, there's likely to be more bugs/vulns out there to be discovered. With effort and care you can safely run this but reducing attack surface is a good idea for defense in depth.