My end result is not to know, for each (x,y) array how many 1's they share just to know what are the top 10 y arrays that share the most 1' with each x array.

Convert your arrays of 0s 1s to bit-strings, then use bitwise-& and unpack '%32b*' to count the equivalences and you can do this 300+ times faster than comparing the arrays:

#! perl -slw
use strict;
use Benchmark qw[ cmpthese ];
use Data::Dump qw[ pp ]; $Data::Dump::WIDTH = 500;

our $I //= -1;
our $N //= 1000;

our @xArrays = map[ map int( rand 2 ), 1 .. 15_000 ], 1 .. $N;
our @yArrays = map[ map int( rand 2 ), 1 .. 15_000 ], 1 .. $N;

our @xStrings = map{ join '', @$_  } @xArrays;
our @yStrings = map{ join '', @$_  } @yArrays;

our @xBits = map{ pack 'b*', $_ } @xStrings;
our @yBits = map{ pack 'b*', $_ } @yStrings;

cmpthese $I, {
    array => q[
        my %top10s;
        for my $x ( 0 .. $#xArrays ) {
            for my $y ( 0 .. $#yArrays ) {
                my $count = 0;
                $xArrays[$x][$_] == 1 && $yArrays[$y][$_] == 1 and ++$
+count for 0 .. $#{ $xArrays[ 0 ] };
                $top10s{"$x:$y"} = $count;
                my $discard = ( sort{ $top10s{$a} <=> $top10s{$b} } ke
+ys %top10s )[ 0 ];
                keys( %top10s ) > 10 and delete $top10s{$discard};
            }
        }
        $I == 1 and pp ' arrays: ', %top10s;
    ],
    strings => q[
        my %top10s;
        for my $x ( 0 .. $#xStrings ) {
            for my $y ( 0 .. $#yStrings ) {
                my $count = ( $xStrings[$x] & $yStrings[$y] ) =~ tr[1]
+[];
                $top10s{"$x:$y"} = $count;
                my $discard = ( sort{ $top10s{$a} <=> $top10s{$b} } ke
+ys %top10s  )[ 0 ];
                keys( %top10s ) > 10 and delete $top10s{$discard};
            }
        }
        $I == 1 and pp 'strings: ', %top10s;
    ],
    bits => q[
        my %top10s;
        for my $x ( 0 .. $#xBits ) {
            for my $y ( 0 .. $#yBits ) {
                my $count = unpack '%32b*', ( $xBits[$x] & $yBits[$y] 
+);
                $top10s{"$x:$y"} = $count;
                my $discard = ( sort{ $top10s{$a} <=> $top10s{$b} } ke
+ys %top10s )[ 0 ];
                keys( %top10s ) > 10 and delete $top10s{$discard};
            }
        }
        $I == 1 and pp '   bits: ', %top10s;
    ],
};

__END__
C:\test>1067218 -N=100
               Rate   array strings    bits
array   1.95e-002/s      --    -98%   -100%
strings      1.08/s   5417%      --    -82%
bits         5.97/s  30510%    455%      --
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