I don't think that it really matters, because your script will be limited by IO, not by CPU.

However you can get rid of a bit of duplication for example by writing the file handles to an array, something along these lines:

use strict;
use warnings;
use autodie qw(open);

my @handles;
open $handles[0], '>>', '0_999';
open $handles[1], '>>', '1000_1999';
open $handles[2], '>>', '2000_2999';
$/="//\n";
while (<>) {
   print { $handles[int(($. - 1)/ 1000)] } $_;
}
[download]

(untested).