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.

To the best of my recollection, \A \z \Z were introduced with Perl 5, sometime prior to 1996.

Not quite. \z at least was introduced with perl 5.005 in 1998. I believe that the others do predate this, however.