I was told that || was old and no longer acceptable

No longer acceptable for what?

or and || are not equivalent. They have different precedence.

There are situations where || lends itself better:

$x = $y || $z;       # ok
$x = ( $y || $z );   # ok (unrequired parens)
$x = $y or $z;       # XXX
$x = ( $y or $z );   # ok
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$x = $y or $z;
   means
( $x = $y ) or $z;
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And there are situations where or lends itself better:

open my $fh, '<', $qfn  or die;  # ok
open(my $fh, '<', $qfn) or die;  # ok (unrequired parens)
open my $fh, '<', $qfn  || die;  # XXX
open(my $fh, '<', $qfn) || die;  # ok
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open my $fh, '<', $qfn  || die;
   means
open my $fh, '<', ( $qfn  || die );
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