my %file1_hosts = (
   bobssite => {
      'bobssite.autossl.net' => 1,
      'www.bobssite.com'     => 1,
      'bobssite.dealer.net'  => 1,
   },
   billssite => {
      'billssite.autossl.net'  => 1,
      'www.billssite.com'      => 1,
      'www.billsothersite.com' => 1,
      'bobssite.dealer.net'    => 1,
   },
);
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Then you can easily compare the two files.

sub compare_aliases {
   my ($host, $file1_aliases, $file2_aliases) = @_
   my %aliases = map { $_ => 1 }
      keys(%$file1_aliases),
      keys(%$file2_aliases);
   for my $alias (keys(%aliases)) {
      if (!$file1_aliases->{$alias}) {
         ...
      }
      elsif (!$file2_aliases->{$alias}) {
         ...
      }
   }
}

sub compare_hosts {
   my ($file1_hosts, $file2_hosts) = @_
   my %hosts = map { $_ => 1 }
      keys(%$file1_hosts),
      keys(%$file2_hosts);
   for my $host (keys(%hosts)) {
      if (!$file1_hosts->{$host}) {
         ...
      }
      elsif (!$file2_hosts->{$host}) {
         ...
      }
      else {
         compare_aliases($host,
            $file1_hosts->{$host},
            $file2_hosts->{$host},
         );
      }
   }
}

compare_hosts(\%file1_hosts, \%file2_hosts);
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Update: Small bug fixes.

different approach (just idea):

# load files into alias => id pairs:
my $file1 = {
  'bobssite.autossl.net' => 'bobssite',
  ...
};

my $file2 = { ... };

my @different_aliases = grep exists $file1->{$_} and $file1->{$_} ne $
+file2->{$_}, keys %$file2;

delete $file1{keys %$file2};

my @aliases_not_in_file2 = keys %$file1;
my @ids_not_in_file2 = do {
  my %tmp;
  @tmp{values %$file1} = values %$file1;

  keys %tmp;
};
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I won't get into using a proper parser, aside from saying that anything less than a well-tested parsing module could become difficult to maintain if the data set starts throwing formats that you're not anticipating.

Getting to your question, the first part is basically asking to determine if file1's host ID's are a subset of file2's. Tackle that question first. Pull your ID's from file2 into a hash, where the ID is the hash key. The value for each hash key should be a reference to an anonymous hash containing only the alias's that start with 'www.' For example:

$file2{billsite} = {
    'www.billsouthersite.com' => '',
    'www.billsite.com'        => '',
};
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You don't really need the 2nd level hash to have values; you're only interested in the keys for quick lookups. Once you've pulled file2 into a hash of this nature, the next step is to iterate through file1. when you process one ID, you'll check to see if it's in %file2. If not, fail. Next you'll process each host-alias that fall under the ID you're processing in file1. As you do so, keep a count so that you can be sure that the quantity matches the number of keys of the 2nd level of the HoH %file2. For each host-alias in file1, check your HoH %file2 to see if that key exists under your current ID. If the key exists, and your keycount matches your file1 host-alias count for that ID, that record passes. If at any point there is a mismatch (not enough keys host-aliases, or a host-alias from file1 not found in file2, you can last or die out of your loop and fail without continuing to test.

Once you visualize the datastructure the rest should come easy.

If you need them to be the same, copy the canonical one to the non-canonical one. If you need to know how they differ, and they are guaranteed to have the same order, use diff or something similar.

One way I might do it by hand if I felt I had to is to make a hash of hashes, parse the first file into it, where the host aliases were all keys and their values were say, -1, and then read the second file and add 1 to the value of %hash{hostid}{alias}. This gives you 0 if it's in both, -1 if it's in only the first file, and 1 if it's in only the second file.

#!/usr/bin/perl
use strict;
use warnings;
use Getopt::Long;
use Pod::Usage;

my %alias_hash;
my %host_hash;
my %host_contents;
my %seen;
my $host_id;
my $file1;
my $file2;

GetOptions(
     'h|help'       =>      sub { pod2usage( { -verbose => 1, -input =
+> \*DATA, } ); exit; },
     'm|man'        =>      sub { pod2usage( { -verbose => 2, -input =
+> \*DATA, } ); exit; },
     'f1|file1=s'   =>      \$file1,
     'f2|file2=s'   =>      \$file2,
);
pod2usage( -verbose => 1 ) unless $file1 and $file2;

open(my $file1_handle, '<', $file1) or die "Could not open $file1 ($!)
+\n";
while (my $line=<$file1_handle>) {
    chomp $line;
    if ($line =~ /host id="(.*?)"/)
    {
        $host_id = $1;
    }
    if ($line =~ m{<host-alias>(www.*?)</host-alias>})
    {
        $alias_hash{$host_id}{$1} = -1;         
    }
    if (!$seen{$host_id}) {
        $host_hash{$host_id} = -1;
    }
    $seen{$host_id} = 1;
}
close $file1_handle;
%seen=();

open(my $file2_handle, '<', $file2) or die "Could not open $file2 ($!)
+\n";
while (my $line=<$file2_handle>) {
    chomp $line;
    if ($line =~ /host id="(.*?)"/)
    {
        $host_id = $1;
    }
    if ($line =~ m{<host-alias>(www.*?)</host-alias>})
    {
        $alias_hash{$host_id}{$1}++;  
    }
    if (!$seen{$host_id}) {
        $host_hash{$host_id}++;
    }
    $seen{$host_id} = 1;
}
close $file1_handle;

for my $k1 ( keys %alias_hash ) {
    for my $k2 ( keys %{ $alias_hash{$k1} } ) {
         print "$k2 exists in only $file1\n" if $alias_hash{$k1}{$k2} 
+== -1;
         print "$k2 exists in only $file2\n" if $alias_hash{$k1}{$k2} 
+== 1;
    }
}
while ( my ($key, $value) = each(%host_hash) ) {
    print "$key exists in only $file1\n" if $host_hash{$key} == -1;
    print "$key exists in only $file2\n" if $host_hash{$key} == 1;
}
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