Why not support both ID versions pointing at a single resource?
I'm somewhat inclined to say if we're uniquely identifying resources with a unique, human-readable string, that's the ID you should always use to refer to things. It seems slightly more complicated to explain to users that there are these two ways to refer to things.
There's also the issue (or benefit) of keeping the UUID the same if you are able to change the human-readable ID.
And don't even get me started on auth checks and someone spoofing the system because something still accepts the old identifier long after the original owner gave it up and some malicious party grabs it.