# open your file 1 as $IN1...
my %hash_file_1;
while (<$IN1>) {
     if (/entry) {
          my $key = $_;
          my $value = "";
          while (<$IN1>) {
              last if /EOE/;
              $value .= $_;
          }
          $hash_file_1{$key} = $value;
     }
}
# open file 2 as $IN2
while (<$IN2>) {
     if (/entry) {
          my $key = $_;
          if (exists $hash_file_1{$key}) {
               my $value2 = "";
               while (<$IN2>) {
                    last if /EOE/;
                    $value2 .= $_;
               }
              # do the comparison between $value2 and $hash_file_1{$key}
              # and print what you need
          }
     }
}

##</code><code>##

# open your file 1 as $IN1...
my %hash_file_1;
while (<$IN1>) {
     if (/entry) {
          my $key = $_;
          my $value = read_entry($IN1);
          $hash_file_1{$key} = $value;
     }
}
# open file 2 as $IN2
while (<$IN2>) {
     if (/entry) {
          my $key = $_;
          if (exists $hash_file_1{$key}) {
               my $value2 = read_entry($IN2);
              # do the comparison between $value2 and $hash_file_1{$key}
              # and print what you need
          }
     }
}

sub read_entry {
     my $FH = shift;
     my $value;
     while (<$FH>) {
          return $value if /EOE/;
          $value .= $_;
     }
}

##</code><code>##

sub read_entry {
     my $FH = shift;
     my @value_arr;
     while (<$FH>) {
          return \@value_arr if /EOE/;
          chomp; # might not be needed, will depend on what will be done next with the array of lines
          push @value_arr, $_;
     }
}