This is kind of like saying a tractor is safer than a car. LXD does not have the same feature set as docker or k8s.
If all you want is a more secure docker then podman got you covered.
If you want more secure k8s then you will have to wait a bit I guess for https://github.com/rootless-containers/usernetes but the cri-o runtime for k8s does have a rootless mode.
LXD is not a replacement for docker or for k8s as it offers a different feature set from both of those.
Last I wanted what one of the features it offered, which is a persistent whole OS container, I tried to install LXD on fedora, and after trying to get lxc running, failing to do so and seeing it's horror show of a systemd setup while debugging [1], I looked elsewhere and instead settled for rootless podman with --rootfs.
[1] https://github.com/lxc/lxc/blob/master/config/init/systemd/l... does something which ubuntu is very fond off and is the main reason why I stopped using it. They call sysv-style init scripts like https://github.com/lxc/lxc/blob/master/config/init/sysvinit/... from systemd and in my experience this obsecures errors as somethign ends up failing but via systemd it still looks like it is running.