I take it this is bowtie output? It makes no sense to me why you are comparing all IDs in the first file to all IDs in the second? The whole point of using a hash is that you can look up specific keys, whereas an array would be for storing an ordered list.

What are you actually trying to do? Get the common IDs between the files and say whether their associated sequences match? You can try something like this for that :

foreach my $id (keys %hash1){ # you can use (sort keys %hash1) if you 
+want them in a specified order
   if ( exists $hash2{$id} ){
      print "\'$id\' exists in both hashes.\n";
      if ( $hash1{$id} eq $hash2{$id} ){
         ## id and sequence are stored as key value pairs
         print "and the sequences match too.\n";
      }
      else{
         print "but the sequences do not match.\n";
      }
   }
   else {
      print "\'$id\' only exists in hash1.\n";
}

}
[download]

If you want help with data strucutes, try perldsc for starters.