My personal regex best practices (solidly in line with TheDamian's as given in his PBP book) include reserving  ^ $ for matching around embedded newlines (which means that the  /m regex modifier is always asserted) and using  \A \z \Z as "absolute" string start/end anchors. To the best of my recollection,  \A \z \Z were introduced with Perl 5, sometime prior to 1996 (update: but see hippo's correction).

... is there something which "\Z" can do which "$" does not??

It's the other way around:  ^ $ match also around embedded newlines (with the ever-present  /m modifier), while  \A \z \Z match only at string start/end; hence, in a sense, they do less. The advantage of this practice is that you never have to think about what  ^ $ do; also,  \A \z \Z cannot be modified.