Here are my results, first with your "a" .. "daaa", and then with a much smaller dataset ("a".."daa", only 2731 values), and finally with just "a" .. "aa" (27 values).

#!/usr/bin/perl
use strict;
use warnings;

use List::Util qw/ maxstr /;
use Benchmark qw/ cmpthese /;

my @vals = reverse "a" .. "daa";

cmpthese( -10, {
    sorting => sub {my $max = pop @{[sort @vals]}},
    iterating => sub {
        my $max = $vals[0];
        $max = ( $_ gt $max ) ? $_ : $max foreach @vals;
    },
    list_util => sub {my $max = maxstr @vals}
    });
__END__
              Rate    sorting  iterating list_utils
sorting    0.659/s         --       -42%       -82%
iterating   1.13/s        72%         --       -69%
list_util   3.67/s       458%       224%         --

             Rate    sorting  iterating list_utils
sorting     537/s         --       -32%       -80%
iterating   789/s        47%         --       -70%
list_util  2661/s       395%       237%         --

               Rate    sorting  iterating list_utils
sorting     50180/s         --       -25%       -78%
iterating   66991/s        34%         --       -70%
list_utils 225804/s       350%       237%         --
[download]

So in all cases, using the built in List::Util proceedure was quite a bit more than twice as fast as either of the others. And it's also much simpler to use, so it seems like something of a no-brainer to me.