You are right. See the following benchmarks:

use strict;
use warnings;
use Benchmark 'cmpthese';

sub create { map {rand() < $_[1] ? 1 : 0} 1..$_[0] }

sub compare1 { # naive
  my $x = shift;
  my $n = shift;
  return map { my $y=$_; scalar grep { $y->[$_] == 1 and $x->[$_] == 1
+ } 0..$n-1 } @_;
}

sub compare2 { # first find 1s in x, then check in ys
  my $x = shift;
  my $n = shift;
  my @nxs = grep { $x->[$_] } 0..$n-1;
  return map { my $y=$_; scalar grep { $y->[$_] == 1 } @nxs } @_ ;
}

sub compare3 { # stringify
  my $x = shift;
  $x = join '', @$x;
  return map { my $j = $x & join'',@$_; $j =~ tr/1/1/ } @_;
}

my $n  = 15000;
my $p  = 0.005;
my $ny = 10;
my @x = create $n, $p;
my @ys = map { [ create $n, $p ] } 1..$ny;

my @r1 = compare1 \@x, $n, @ys;
my @r2 = compare2 \@x, $n, @ys;
my @r3 = compare3 \@x, @ys;
print "compare1: @r1\n";
print "compare2: @r2\n";
print "compare3: @r3\n";

cmpthese( -5, { compare1 => sub{ compare1 \@x, $n, @ys },
                compare2 => sub{ compare2 \@x, $n, @ys },
                compare3 => sub{ compare3 \@x, @ys },
              }
        );
[download]

           Rate compare1 compare3 compare2
compare1 48.8/s       --     -81%     -91%
compare3  253/s     420%       --     -53%
compare2  537/s    1002%     112%       --
[download]