OK, BrowserUK, here we go with a sameFringe function and the test data copied from your posted solution.

Note that I had to make a small change in my closure (unshift instead of push on the @ref_list array), because my original code did not compare $a and $c correctly (the leaves were appearing in opposite order).

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

my $a = [ 1, [ 2, [ 3, [ 4, 5 ] ] ] ];
my $b = [ 1, [ [ 2, 3 ], [ 4, 5 ] ] ];
my $c = [ [ [ [ 1, 2 ], 3 ], 4 ], 5 ];

sameFringe( $a, $a );
sameFringe( $a, $b );
sameFringe( $a, $c );

my $x = [ 1, [ 2, [ 3, [ 4, [ 5, 6 ] ] ] ] ];
my $y = [ 0, [ [ 2, 3 ], [ 4, 5 ] ] ];
my $z = [ 1, [ 2, [ [ 4, 3 ], 5 ] ] ];

sameFringe( $a, $x );
sameFringe( $a, $y );
sameFringe( $a, $z );

sub sameFringe {
    my $next_el1 = create_iterator(shift);
    my $next_el2 = create_iterator(shift);
    my $match = 1;
    while (1) {
        my $left = $next_el1->();
        my $right = $next_el2->();
        no warnings 'uninitialized';
        print $left, " ", $right, "\n";
        unless ($left eq $right) {$match = 0 ; last} ;
        last unless defined $left;
    }
    $match ? print "the trees match\n": print "the trees don't match\n
+";
}

sub create_iterator {
    my $ref = shift;
    my @ref_list;
    return sub {
        while (ref $ref eq 'ARRAY') {
            unshift @ref_list, @$ref;
            $ref = shift @ref_list;
        } 
        my $leaf = $ref;
        $ref = shift @ref_list;
        return $leaf;
    }
}
[download]

The following is the output:

>perl fringe.pl
1 1
2 2
3 3
4 4
5 5

the trees match
1 1
2 2
3 3
4 4
5 5

the trees match
1 1
2 2
3 3
4 4
5 5

the trees match
1 1
2 2
3 3
4 4
5 5
 6
the trees don't match
1 0
the trees don't match
1 1
2 2
3 4
the trees don't match
[download]

Laurent_R++ Another solution that works and (almost) meets the specs.

It would be easier to compare with other attempts if you wrapped your algorithm up in a sameFringe() subroutine -- same args and return -- as is used in the linked article.

It is also a good idea to test using the same tests as they use. They have been quite carefully designed (or arrived at) to test several particular edge cases.