I suspect the issue is because you are using chop instead of chomp. If your input files are not newline terminated, your chops will remove data values from the terminating entry. The code:

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

my @file1 = qw(
    1.10.10
    1.10.1040
    1.10.150
    1.10.220
);

my @file2 = qw(
    1.10.10.640
    1.10.10.650
    1.10.10.660
    1.10.1040.20
    1.10.150.290
    1.10.150.300
    1.10.150.310
    1.10.220.80
);

for(my $i=0; $i<@file1; $i++)
{
    chomp($file1[$i]);
    #print "F $file1[$i]";

    for(my $j=0; $j<@file2; $j++)
    {
        chomp($file2[$j]);
    
        my @array = split(/\./, $file2[$j]);
    
        my $cat = "$array[0]" . "." . "$array[1]" . "." . "$array[2]";
    
        if("$file1[$i]" eq "$cat")
        {
            print "$file1[$i] $cat\n";
        }
    
    }
}
[download]

(with null-op chomps) yields the result

1.10.10 1.10.10
1.10.10 1.10.10
1.10.10 1.10.10
1.10.1040 1.10.1040
1.10.150 1.10.150
1.10.150 1.10.150
1.10.150 1.10.150
1.10.220 1.10.220
[download]

which seems to my eyes to be the spec. There are some stylistic modifications I would implement (Foreach Loops, hash instead of iterating with eq), but this should fix your bug.

Update: I'd missed that you were chopping in an inner loop, as ikegami notes below. The bug fix still holds.