As an example, I have used the absolute value function abs but I could have used abs($_). Which is best? Does it matter?

Specifically on this point: others have pointed out that there is no difference functionally, so that leaves style and clarity to drive the choice.

In my case, I hardly ever use the abs function (despite the fact that most of the code I write is maths-related). Because of that, I would choose always to write $abs = abs($_); rather than $abs = abs; - for the latter, I'd have to stop and think a few deciseconds longer any time I wrote it or read it.

On the other hand, for functions that default to $_ that I use commonly, I'm much more likely to prefer the short form.

On the gripping hand, I try to avoid over-reliance on $_. Normal for loops are almost always improved by naming the variable. I mostly have $_ in "right-to-left" code - maps, greps, modifier-for - and there, again, I look to name a variable if I'm going to be using it several times:

# different $_ on left and right, but I find this perfectly clear
$sum += $_ for /(\d)/g;
# or
my @saints = grep $_->is_saint, @users;
# or
my @users = map {
  my $name = $_;
  is_god($name)
    ? find_with_sacrifice($name, $spare_user)
  : is_saint($name)
    ? find_with_relic($name, $relic)
  : $spare_user
    ? find_user($name)
  : do {
    # save for later
    $spare_user = find_user($name);
    ()
  }
} @names;
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