I used to use LXC maybe 5 years ago but I've since replaced everything with docker/compose. The main difference between LXC and Docker is that LXC is meant to be more like a Virtual Machine than a container. LXC containers run their own instance of systemd and can run multiple processes easily. Docker is meant to run a single process although people sometimes do hacks with supervisord or s6 overlay to run multiple processes.
At the time LXC didn't really have a concept of images like Docker, it was just base images like Ubuntu 18.04 or Debian 9 and you'd shell in the container and install your stuff.
LXD is a tool built on top of LXC, confusingly enough the LXD client is called lxc... It's higher level and might have the ability to use images, not sure, I never felt the need to learn it.
I've always used lxc and only recently tried docker.
I really cant wrap my head around all the crazy shit docker alters on your network settings like rewriting a bunch of firewall rules without telling you
Not sure if i was doing something wrong but that was my experience with docker
I love it. It's like a cross between virtual box and docker. You get a container that spins up fast but behaves more like a vm. You can install services, you get an ip address, etc.