Javascript两个日期时间比较问题

我试图用javascript比较两个日期。实际上，我的目标得到警告信息，如果第一次约会大于第二次约会，但javascript不能正常工作。当我调试火狐游标去else块，即使发生条件。同时，类似的javascript代码可以在jsfiddle上正常工作。

http://jsfiddle.net/Mjora/ZNaMW/

Javascript代码

$("#btn").click(function(){
    var firstDate = $('#firstDate').val();
    var lastDate = $('#lastDate').val();
    if (firstDate > lastDate) {
        alert("First date can not be greater than Last date!!");
    }
    else{...} 
});

我也试过这样的代码;

   $("#btn").click(function(){
        var firstDate = $('#firstDate').val();
        var lastDate = $('#lastDate').val();
        if (new Date(firstDate) > new Date(lastDate)) {
            alert("First date can not be greater than Last date!!");
        }
        else{...} 
    });
 /********/
var fDate="10.10.2020";
var lDate="10.10.2010";
var fDateSpl= fDate.Split(".");
var lDateSpl= lDate.Split(".");
var newFDate = new Date(fDateSpl[2], fDateSpl[1], fDateSpl[0]);
var newLDate = new Date(lDateSpl[2], lDateSpl[1], lDateSpl[0]);

if (newFDate > newLDate) {
    alert("First date can not be greater than Last date!!");
}
else{...} 

<input type="text" id="firstDate"/>
    <br/>
<input type="text" id="lastDate"/>
    <br/>
<input type="button" value="Send" id="btn"/>

$("#btn").click(function(){
    var firstDate = $('#firstDate').val();
    var lastDate = $('#lastDate').val();
    if (Date.parse(firstDate) > Date.parse(lastDate)) {
        alert("First date can not be greater than Last date!!");
    } 
});

var fDateSpl= fDate.Split(".");
var lDateSpl= lDate.Split(".");

var fDateSpl= fDate.split(".");
var lDateSpl= lDate.split(".");