It's been a while since I looked at kuik, but I would say the main difference is that Spegel doesn't do any of the pulling or storage of images. Instead it relies on Containerd to do it for you. This also means that Spegel does not have to manage garbage collection. The nice thing with this is that it doesn't change how images are initially pulled from upstream and is able to serve images that exist on the node before Spegel runs.

Also it looks kuik uses CRDs to store information about where images are cached, while Spegel uses its own p2p solution to do the routing of traffic between nodes.

If you are running k3s in your homelab you can enable Spegel with a flag as it is an embedded feature.