If two timestamps share a date from which time zone's perspective: any time zone or a specific time zone?

The former requires checking if the time stamps are within 24 hours of each other.

The latter requires comparing the dates of the time stamps after converting the time stamps to the specific time zone.

use strict;
use warnings;

use DateTime::Format::DateParse qw( );

sub same_date_anywhere {
   my ($dt1, $dt2) = @_;
   ($dt1, $dt2) = ($dt2, $dt1) if $dt1 < $dt2;
   $dt1 = $dt1->clone(); 
   $dt1->subtract( hours => 24 );
   return $dt1 < $dt2;
}

sub same_date_somewhere {
   my ($dt1, $dt2, $tz) = @_;
   for my $dt ($dt1, $dt2) {
      ( $dt = $dt->clone() )
         ->set_time_zone($tz)
         ->truncate( to => 'days' );
   }

   return $dt1 == $dt2;
}

my $dt1 = DateTime::Format::DateParse->parse_datetime("Fri, 26 Aug 201
+1 14:34:55 GMT");
my $dt2 = DateTime::Format::DateParse->parse_datetime("Sat, 27 Aug 201
+1 07:03:02 +1000");

say(same_date_anyhere($dt1, $dt2) ?1:0);
say(same_date_somewhere($dt1, $dt2, $dt1->time_zone) ?1:0);
say(same_date_somewhere($dt1, $dt2, $dt2->time_zone) ?1:0);
say(same_date_somewhere($dt1, $dt2, "America/New_York") ?1:0);
say(same_date_somewhere($dt1, $dt2, "UTC") ?1:0);
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Untested.