• diff $i $j doesn't compare the strings $i and $j, but interprets them as file names. I see no indication in your textual description that that's the goal. If you just want to compare strings for equality, use $i eq $j in Perl.
• `program > /dev/null` doesn't make any sense to me. First throw away the output, then capture it, then discard it again by putting it in void context...
• Since each `...` line starts its own shell, the exit status from diff command won't be available in `$?`.

If you only want to compare each line of tst1 to the corresponding line in tst2 you don't need two loops. Use something like this:

while (@tst1)
{
  $i= shift @tst1;
  $j= shift @tst2;
  chomp($i);
  chomp($j);
 `diff $i $j > /dev/null`;
 `echo $?`;
}
[download]

You thought you needed two loops because you wanted to step through two arrays, but you need only one loop that makes a simultaneous step through both arrays.

Thanks jethro and all , this seemed to work

#! /usr/bin/perl
use File::Compare;
open (IF,"<tst1");
open (IF2,"<tst2");
my(@tst1) = <IF>;
my(@tst2) = <IF2>;
my ($i);
my ($j);
while (@tst1)
{
 $i=shift @tst1;
 $j= shift @tst2;
 chomp($i);
 chomp($j);
 #print "$i\n";
 #print "$j\n";
 if (compare("$i","$j") == 0) {
 print "$i $j are equal\n";
 }
 else
 {
 print "$i $j are not equal\n";
 }
}
close(IF);
close(IF2);
[download]

use strict;
use warnings;
use File::Basename;

my @tst1 = qw(
    /dir1/file1
    /dir1/file2
    /dir1/file3
);

my @tst2 = qw(
    /dir2/file1
    /dir2/file2
    /dir2/file3
);

chomp @tst1;
chomp @tst2;

for my $t1 (@tst1) {
    for my $t2 (@tst2) {
        next unless basename($t1) eq basename($t2);
        my $status = system "diff $t1 $t2 > /dev/null";
        print "$status\n";
    }
}
[download]

#!/usr/bin/perl

use strict;
use warnings;
use File::Compare;
use File::DirCompare;
use Text::Diff;
use Text::Diff::Table;
use YAML;
use YAML::Dumper;

my $dir1 = '/usr/lib/perl5/5.8.8/CGI';
my $dir2 = '/usr/lib/perl5/5.8.8/Shell';

File::DirCompare->compare($dir1, $dir2, sub {
    my  ($a, $b) = @_;
    if (! $b) {
        printf "Only in %s: %s\n", dirname($a), basename($a);
    }
    elsif (! $a) {
        printf "Only in %s: %s\n", dirname($b), basename($b);
    }
    else {
        print "Files $a and $b differ\n";
    }
});

if ($dir1 eq $dir2) {
    print "They're equal\n";
} 
else {
    print "They're not equal\n";
}     

my $tst1 = '/usr/lib/perl5/5.8.8/CGI.pm';
my $tst2 = '/usr/lib/perl5/5.8.8/Shell.pm';

my $diff = Text::Diff::Table->new;
$diff = diff $tst1, $tst2, { STYLE => "Table" };

my $dumper = YAML::Dumper->new;
$dumper->indent_width(4);
print $dumper->dump($diff); 

if (compare($tst1, $tst2) == 0) {
    print "They're equal\n";
}
else {
    print "They're not equal\n";
}
[download]

Why not just use the diff utility?

That is confusing advice, given the fact that the OP is already using diff. I believe the question is how to use it to avoid unexpected behavior (which the OP did not clearly specify).