Well, taking nothing for granted (note, I did try larger arrays, fewer iterations, etc , and still got similar results):

use Benchmark;

my @arr=(0..10000);

open(FH1, '>file1') or die "file1: $!";
open(FH2, '>file2') or die "file2: $!";
open(FH3, '>file3') or die "file3: $!";

timethese(100, {
BIGJOIN=>\&bigjoin,
ITERATE=>\&iterate,
MAPIT=>\&mapit,
});

close FH1;
close FH2;
close FH3;

sub bigjoin {
 print FH1 join("\n", @arr, '');
}

sub iterate {
 print FH2 "$_\n" for @arr;
}

sub mapit {
 print FH3 map "$_\n" @arr;
}

>perl tst
Benchmark: timing 100 iterations of BIGJOIN, ITERATE, MAPIT...
   BIGJOIN:  3 wallclock secs ( 3.41 usr +  0.00 sys =  3.41 CPU) @ 29
+.33/s (n=100)
   ITERATE: 14 wallclock secs (13.57 usr +  0.00 sys = 13.57 CPU) @  7
+.37/s (n=100)
     MAPIT: 17 wallclock secs (16.86 usr +  0.00 sys = 16.86 CPU) @  5
+.93/s (n=100)
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