Excellent!
The rule of thumb for most date and time calculations is to normalize both moments to UTC first, then perform the math. But in this case, it really only makes sense to compare dates from the perspective of a specific local time. It's easy to imagine a practical application for wanting to know if two moments at two different places in the world occurred on the same date reckoned from Sydney, Australia. It's not as easy to imagine a practical application for wanting to know if two moments occurred on the same date reckoned from UTC, which is abstract. Who would care?
Consider this very light refactoring:
#!perl
use strict;
use warnings;
use DateTime;
use DateTime::Format::DateParse;
@ARGV == 2 or die "Usage: perl $0 <timestamp 1> <timestamp 2>\n";
my $ts1 = shift;
my $ts2 = shift;
my $tz = 'Australia/Sydney';
my $dt1 = DateTime::Format::DateParse->parse_datetime($ts1)
->set_time_zone($tz);
my $dt2 = DateTime::Format::DateParse->parse_datetime($ts2)
->set_time_zone($tz);
my $diff = $dt1->delta_days($dt2)->delta_days();
print "$dt1 delta $dt2 is $diff days\n";
exit 0;