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

my %file2;
open my $file2, '<', '/home/match_miss' or die "Couldn't open file2: $
+!";
while ( my $line = <$file2> ) {
    ++$file2{$line};
}

open my $file1, '<', '/home/BIG_FILE' or die "Couldn't open file1: $!"
+;
while ( my $line = <$file1> ) {
    print $line if defined $file2{$line};
}
[download]

print $line if defined $file2{$line};

I think that finds lines in file 1 that are also in file 2. To find lines in file 1 not in file 2, maybe change that to:

print $line unless defined $file2{$line};