It's probably more apt to compare it to Proxmox, Virtuozzo, or VMware, but leveraging containers instead of a hypervisor.
With things like kernel same-page merging, LVM thin storage pools, and memory ballooning, the difference between "containers" and "VMs" is reducing to the point where the main difference is whether there's a software layer emulating the hardware or not.
Docker is the new kid on the block, and a bonfire of billions of VC dollars can create a lot of smoke.
Proxmox does both hypervisors and containers though...I wouldn't say primarily containers.
But that is a better crowd to specifically compare LXD to, rather than docker.
You can mess about and create a docker image to run a full OS, and you can also get LXD/LXC to work for docker use cases. But, you're swimming upstream in doing so.