Currently there is no way to replace "Labels" for a project with custom field of type "Labels" in a slick way.

Main differences:

• The "More Actions" menu will still point to the "Labels" system field, even if you hide the field in the field scheme. That is a major drawback.
• The "cog" icon, available in gadgets, issue navigator, etc., will also still point to the "Labels" system field.

Jira needs to provide server/project admins a facility to link (or replace) the general (system) field with a custom field of type "Labels" for every single project independently.