How to Compare dd/MM/yyyy format date with today's date in javascript

If you date is in string, then you have to split them out into the various date parts by using split[^]method. To avoid this hassle, you should consider using a datepicker like https://jqueryui.com/datepicker/[^]
Next, use the appropriate Date[^] methods to create the date objects.
Try this example and adapt:

<script>
var somedayString = "16/4/2015";
var dateParts= somedayString.split("/");
var day = dateParts[0];
var month = dateParts[1] - 1;
var year = dateParts[2];
// set a date
someday = new Date(year, month, day);
alert("someday is " + someday);

// set a date
var today = new Date();
today.setHours(0,0,0,0);
alert("today is " + today);

if (today < someday) {
    text = "Today is before someday.";
} else if (today > someday) {
    text = "Today is after someday.";
} else {
    text = "Someday is today.";
}
alert(text);
</script>

Note that the month numbers start from 0 which represents January.

// try here
 var currentDate = new Date()
 var day = currentDate.getDate()
 var month = currentDate.getMonth() + 1
 var year = currentDate.getFullYear()
 document.write("" + day + "/" + month + "/" + year + "")
 var todaysDate = day + "/" + month + "/" + year