You are not comparing dates. You are comparing strings. In the world of string comparisons, 09/17/2015 > 01/02/2016 because 09 > 01. You need to either put your date in a comparable string format or compare DateTime objects which are comparable.
<?php
$date_now = date("Y-m-d"); // this format is string comparable
if ($date_now > '2016-01-02') {
echo 'greater than';
}else{
echo 'Less than';
}
Or
<?php
$date_now = new DateTime();
$date2 = new DateTime("01/02/2016");
if ($date_now > $date2) {
echo 'greater than';
}else{
echo 'Less than';
}