Proxmox and LXD both have features that the other does not. It’s worth comparing if you do not use certain features of one or the other.
For example proxmox can set up a ceph cluster for you and you’ll not have to think about anything. Or live-migration for VMs. Also proxmox is more plug & play. After installing you can browse to a web interface for management and deploy a VM right away. LXD requires some manual initial configuration for your network and storage.
LXD on the other hand is incredibly light-weight, can be installed on a distro/hardware of your choosing and is in my opinion way more mature. The docs are really complete. It is way more friendly on your resources, can easily run on a raspberry pi.
If you happen to find a bug and report it, it is very likely to be fixed the same day. If you request a feature it is likely to be put on a relatively short wishlist and added quickly. Proxmox on the other hand has thousands of open bug reports, some even 5 years old, likely never to see a fix.
If you prefer web management over cli you can use https://www.nuber.io/. Manually configure LXD to your liking on the cli and then use this sleek looking web interface to manage your local cloud.
Personally I have used both. I currently have several instances/clusters of both running at the moment. The only reason I have not replaced my proxmox clusters with LXD yet is because of the live migration feature for VMs. As soon as LXD gets that feature it’s bye bye proxmox and never to be seen again.
In my opinion LXD wins hands down