Im under the assumption that asleep but non anchored parts still can be moved around on the client (if client has ownership) around. As for when I have an anchored client part, the parts dont really show movement across the server while anchored.
However if a part can be asleep on the server, and a client has ownership of it and moves it around with its own mini physics, I feel as though that would lag less as roblox’s physics are no longer being applied to it while still having it move around on the server if the client moves it.
I hope this explains it well. If not ill elaborate better.