The LXC project does not refer to itself as low level, but ironically Docker which knows exactly what LXC is, does. And the results are these needless misconceptions, which is a tad unfair to the developers of the LXC project. Why would anyone try LXC if they think its 'low level'?
LXD extends LXC to add a REST api, multi-host container management and soon live migration.
LXC is a full fledged userland project and has been since 2009 when it began development. It is also responsible for driving the development of a lot of the kernel capabilities mainly 'cgroups' and 'namespaces' needed to support containers.
That's the 'low level' capabilities that LXC, Docker. Nspawn use to give you containers, but it would be as inaccurate to refer to Docker as 'low level' because it uses these, as it would LXC.
A container is simply a file system in a folder that gets booted and works on any underlying Linux filesystem so I am not sure about how conceptually a 'container format' fits there? That's one of the great things about containers. You do not need to think about storage. Simply zip the container folder and move across servers. Containers are completely portable across any Linux system today. But if you are going to use aufs or overlayfs layers to build single apps containers with constrained container OS templates then perhaps there is a need for a format.