I'd rather focus on optimizing the size of uuids than their text representation. Shipping uuids around as utf-8 text is silly. They're at most 128bits, so we shouldn't use more than that many.

In the case where it's necessary to have a text representation (e.g. in some user interface) I guess it's fine to choose whatever (stable) transformation you like, but the standard ways specified in RFC-4122 (hexadecimal, with or without hyphens) seem like the most foolproof. Regarding the logs search use case, the first "chunk" of a uuid is usually well more than enough for a unique match, IME.

Also, I've been burned before in cases where some clever transformation was used to make a uuid look different in text form, because in order to synthesize the actual binary uuid I first have to reverse engineer the transformation--e.g. to find the database record corresponding to some http request log message. That's just annoying, and the polar opposite of "user friendly" for the user story of an engineer trying to figure out what's wrong with the system.

So.. I guess my vote is to stick to the standard.