An admin or editor also cannot delete a page, an important distinction. A few years ago, a guy with admin rights to some pages took the other owners off, made himself the owner, deleted the pages, and then left the site. It was ugly and made a lot of work for a few people.
As mrchad9 says, share the page if you trust the person. I happen to know who is asking you, and I am certain he means well.
Owner: There can be only one owner at a time. You can't take away an owner's privileges except by assigning a new owner. Only an owner or an admin can assign a new owner. When a new owner is assigned, the former owner becomes an admin. Only an owner can delete a page.
Admin: Granting a user admin privileges allows them to edit the page, and to add other users as editors and admins. Admins and owners both get credited on the main object page in the "Page By" field. An admin can grant and revoke privileges for any user, including himself and the owner (to revoke the owner's privileges, designate a new owner first).
Edit: Granting a user edit privileges will allow them to make changes to the body of the page.
None: Removes all privileges.