Hi, Vikas, and welcome to PerlMonks!

You've enclosed one loop within another, so you're attempting to compare the first $comp1 value against all elements of @var2, and so on. And tobyink's point about "if they match" is well made, so I suspect you want $comp1 eq $comp2.

Given this, consider the following:

use strict;
use warnings;

my %matchingLines;

open my $fh1, '<', 'File1.txt' or die $!;
chomp( my @file1Lines = <$fh1> );
close $fh1;

open my $fh2, '<', 'File2.txt' or die $!;
chomp( my @file2Lines = <$fh2> );
close $fh2;

for my $file1Line (@file1Lines) {
    $matchingLines{"$file1Line\n"}++
      if $file1Line ~~ @file2Lines;
}

open my $fh3, '>', 'FileA.txt' or die $!;
print $fh3 $_ for keys %matchingLines;
close $fh3;
[download]

If a line in @file1Lines is found in @file2Lines via the smart match operator (works as equality), it's added to the hash %matchingLines for later printing to a file (the hash is used to avoid the possibility of writing multiple instances of the same line to the file).

Hope this helps!

Update: Lotus1 correctly brought to my attention that I misunderstood the OP. Have revised the script.