I find that I (mostly) use the $new = do_something($old) way when I feel that $old and $new often will be different variables.

I tend to use something like

sub do_something_to(\$) {
   ...
}
...
do_something_to($me);
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Note the absense of \ in the call of the function. That is taken care of by the prototype. (Se perlsub for more info on prototypes).

There is no Right Way, there is just "My Way" and "Your Way"...