Joyent's Solaris-derived SmartOS shows how containers (a.k.a zones) can coexist with KVM-based VMs on the same kernel. All modern Linux distros have similar capabilities, if not quite as refined. The battle is about management tools - the company that controls the de-facto standard can make a lot of money, see how VMware gave away ESXi, the real revenue is in vCenter, and value-added features like HA and vMotion.
Both public cloud and hypervisor vendors will gain container capabilities. AWS and Microsoft have already made announcements, the others, including VMware, will follow. It seems to me new applications will be designed for, and run directly in containers, whereas heavyweight VMs will be reserved for migrated legacy workloads. Containers do require automation tools like Puppet/Chef/Ansible/Saltstack to be manageable, however, as does the Cloud. Another opportunity to sell to the enterprise.
The efficiency gains from containers are nothing to sneeze at, you can squeeze an order of magnitude or two more containers than VMs on the same hardware, not a mere 10%. For cloud providers, specially PaaS ones, this is compelling. Even for IaaS, thin provisioning is easier to achieve with containers. Linux based container solutions need to reach the levels of maturity of Solaris, specially as concerns security as the recent Docker vulnerability shows. Using a better file system like ZFS (as done by SmartOS or Flocker) is also a big boost, and can provide something close to vMotion in terms of ability to migrate workloads, if not yet online (shutdown required).
Some of the more important gains are in the realm of latency - SSDs give, and VMs take away. At my company, switching from AWS to a containerized private cloud (OpenIndiana) yielded significant improvements in cost (6x), latency (1/3), throughput (3x) and uptime (MTBF went up 30x).
I've already stated my belief VMware style hypervisors will be relegated to a niche of hosting legacy workloads. Nothing wrong with that, and it can be quite lucrative, as shown by IBM. Container vendors won't be able to extract the same profit margins, because they are built on open-source, so the legacy vendors may still end up gobbling up the new entrants. In other words, legacy workloads may represent a small fraction of future volume, but a large portion of value.