这里有一个更新的答案，http://www.datejs.com/上有一个很好的js库

Datejs是一个开源的JavaScript数据库，用于解析、格式化和处理。

完全满足日期。将字符串转换为RFC822中指定的dd-mm-YYYY格式。 如果使用yyyy-mm-dd解析可能会做错误。

time = "2017-01-18T17:02:09.000+05:30"

t = new Date(time)

hr = ("0" + t.getHours()).slice(-2);
min = ("0" + t.getMinutes()).slice(-2);
sec = ("0" + t.getSeconds()).slice(-2);

t.getFullYear()+"-"+t.getMonth()+1+"-"+t.getDate()+" "+hr+":"+min+":"+sec

//Here pdate is the string date time
var date1=GetDate(pdate);
    function GetDate(a){
        var dateString = a.substr(6);
        var currentTime = new Date(parseInt(dateString ));
        var month =("0"+ (currentTime.getMonth() + 1)).slice(-2);
        var day =("0"+ currentTime.getDate()).slice(-2);
        var year = currentTime.getFullYear();
        var date = day + "/" + month + "/" + year;
        return date;
    }

var temp1 = "";
var temp2 = "";

var str1 = fd; 
var str2 = td;

var dt1  = str1.substring(0,2);
var dt2  = str2.substring(0,2);

var mon1 = str1.substring(3,5);
var mon2 = str2.substring(3,5);

var yr1  = str1.substring(6,10);  
var yr2  = str2.substring(6,10); 

temp1 = mon1 + "/" + dt1 + "/" + yr1;
temp2 = mon2 + "/" + dt2 + "/" + yr2;

var cfd = Date.parse(temp1);
var ctd = Date.parse(temp2);

var date1 = new Date(cfd); 
var date2 = new Date(ctd);

if(date1 > date2) { 
    alert("FROM DATE SHOULD BE MORE THAN TO DATE");
}

查看Moment.js。它是一个现代而强大的库，弥补了JavaScript糟糕的Date函数(或其不足)。