perllocale weirdness, bug, or...?

[Krambambuli]

The following code

#!/usr/bin/perl

use strict;
use warnings;

my $s1 = '[e-mail]';
my $s2 = '[e-mail]';
my $s3 = 'aaa2000';
my $s4 = 'aaa_2000';

no locale;

print "\nNO Locale:\n\n";

if ($s1 gt $s2) {print "$s1 is > $s2\n";}
if ($s1 lt $s2) {print "$s1 is < $s2\n";}
if ($s1 eq $s2) {print "$s1 is = $s2\n";}

if ($s3 gt $s4) {print "$s3 is > $s4\n";}
if ($s3 lt $s4) {print "$s3 is < $s4\n";}
if ($s3 eq $s4) {print "$s3 is = $s4\n";}

use locale;

print "\nWith 'use locale;':\n\n";

if ($s1 gt $s2) {print "$s1 is > $s2\n";}
if ($s1 lt $s2) {print "$s1 is < $s2\n";}
if ($s1 eq $s2) {print "$s1 is = $s2\n";}

if ($s3 gt $s4) {print "$s3 is > $s4\n";}
if ($s3 lt $s4) {print "$s3 is < $s4\n";}
if ($s3 eq $s4) {print "$s3 is = $s4\n";}

prints out

NO Locale:

[e-mail] is < [e-mail]
aaa2000 is < aaa_2000

With 'use locale;':

[e-mail] is > [e-mail]
aaa2000 is < aaa_2000

which I cannot really follow. Am I missing something more or less obvious, or is this a bug? Can others confirm to see the same behavior ?

I see this both on a 5.8.8 Perl as on a 5.10.1 Perl.

Many thanks in advance,