Comparing digests of the data is one way to do this i.e.

use strict;
use warnings;

use Digest::SHA;

open my $in_1, '/tmp/f1.txt';
open my $in_2, '/tmp/f2.txt';

my $hash1 = Digest::SHA::sha1_hex(
        do { local $/; <$in_1> }
);

my $hash2 = Digest::SHA::sha1_hex(
        do { local $/; <$in_2> }
);

die "The files are NOT the same\n" unless $hash1 eq $hash2;
print "The file contents are identical\n";
[download]

If your files are really large i.e. in the order of a few gigabytes you could use md5sum on the command line to compare the files instead :

md5sum file1 file2 file3 etc
[download]

Identical files will yield identical hashes. This is useful because you do not have to load the entire file into memory first.