for our $n ( map 10**$_, 1, 3, 6 ) {
    print "Benchmarking $n values";
    our @n = map int( rand $n ), 1 .. $n;
    cmpthese -log $n, {
        sort => q[ 
            my $t = $n >> 1; 
            my @m = sort{ $a<=>$b } @n; 
            my $c=0; 
            $c++ while $m[ $c ] <= $t; 
            my $pct= ( @m - $c ) / @m * 100; 
        ],
        grep => q[ 
           my $t = $n >> 1; 
           my $pct = grep({ $_ > $t } @n ) / @n * 100; 
        ],
    };
};;

Benchmarking 10 values
         Rate sort grep
sort 285546/s   -- -62%
grep 751484/s 163%   --

Benchmarking 1000 values
        Rate sort grep
sort  3525/s   -- -71%
grep 12328/s 250%   --

Benchmarking 1000000 values
       Rate sort grep
sort 1.13/s   -- -90%
grep 11.4/s 911%   --
[download]

Seeing the amount of Perl code involved outside the sort, makes sense. Thanks. Note that sorting is still faster than the original

use strict;
use warnings;

use Benchmark qw( cmpthese );

for our $n ( map 10**$_, 1, 3, 6 ) {
    print "Benchmarking $n values\n";
    our @n = map int( rand $n ), 1 .. $n;
    cmpthese -log $n, {
        orig => q[
            my $c=0;
            for my $elem (@n) {
                if ($elem > $t){
                    $c++;
                }
            }
            my $pct= ( @n - $c ) / @n * 100;
        ],
        sort => q[
            my $t = $n >> 1;
            @n = sort{ $a<=>$b } @n;
            my $c=0;
            $c++ while $n[ $c ] <= $t;
            my $pct= ( @n - $c ) / @n * 100;
        ],
        grep => q[
           my $t = $n >> 1;
           my $pct = grep({ $_ > $t } @n ) / @n * 100;
        ],
    };
}
[download]

Benchmarking 10 values
         Rate orig sort grep
orig 272566/s   -- -11% -41%
sort 306129/s  12%   -- -34%
grep 462968/s  70%  51%   --
Benchmarking 1000 values
       Rate orig grep sort
orig 4332/s   -- -42% -44%
grep 7459/s  72%   --  -4%
sort 7795/s  80%   5%   --
Benchmarking 1000000 values
^C
[download]

Lots of variation in the results due to the random input. The first test with orig I ran actually showed sort as being the fastest, although it usually isn't.

You 'orig' variation never sets $t, but I don't think that matters much. Anyway, I made a slight variation, to reduce the chance the PRNG favours one method over the other:

use strict;
use warnings;
     
use Benchmark qw( cmpthese );
        
for our $n ( map 10**$_, 1, 3, 6 ) {
    print "Benchmarking $n values\n";
    my $l = int log $n;
    our @data = ();
    our @target = ();
    foreach (1 .. $l) {
        push @data, [map int rand $n, 1 .. $n];
        push @target, int rand $n;
    }
    cmpthese -log $n, {
        orig => q[
            for (my $i = 0; $i < @data; $i++) {
                my $c = 0;
                for my $elem (@{$data[$i]}) {
                    $c++ if $elem > $target[$i];
                }
                my $pct= (@{$data[$i]} - $c ) / @{$data[$i]} * 100;
            }
        ],
        sort => q[
            for (my $i = 0; $i < @data; $i++) {
                my $c = 0;
                my @n = sort {$a <=> $b} @{$data[$i]};
                $c++ while $n[$c] <= $target[$i];
                my $pct= (@{$data[$i]} - $c ) / @{$data[$i]} * 100;
            }
        ],
        grep => q[
            for (my $i = 0; $i < @data; $i++) {
                my $pct = grep({$_ > $target[$i]} @{$data[$i]})
                          / @{$data[$i]} * 100;
            }
        ],
    };
}
[download]

This shows 'sort' to be always slower, and 'grep' always winning:

Benchmarking 10 values 
        Rate sort orig grep
sort 34448/s   -- -11% -53%
orig 38503/s  12%   -- -47%
grep 72551/s 111%  88%   --
Benchmarking 1000 values
      Rate sort orig grep
sort 162/s   -- -57% -62% 
orig 381/s 135%   -- -11%
grep 427/s 164%  12%   --
Benchmarking 1000000 values
            (warning: too few iterations for a reliable count)
            (warning: too few iterations for a reliable count)
            (warning: too few iterations for a reliable count)
     s/iter sort orig grep
sort   31.2   -- -83% -85%
orig   5.18 502%   -- -10%
grep   4.67 567%  11%   --
[download]