===
is not necessary. You know both values are strings so you dont need to compare types.
function do_check()_x000D_
{_x000D_
var str1 = $("#textbox1").val();_x000D_
var str2 = $("#textbox2").val();_x000D_
_x000D_
if (str1 == str2)_x000D_
{_x000D_
$(":text").removeClass("incorrect");_x000D_
alert("equal");_x000D_
}_x000D_
else_x000D_
{_x000D_
$(":text").addClass("incorrect");_x000D_
alert("not equal");_x000D_
}_x000D_
}
_x000D_
.incorrect_x000D_
{_x000D_
background: #ff8888;_x000D_
}
_x000D_
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>_x000D_
_x000D_
<input id="textbox1" type="text">_x000D_
<input id="textbox2" type="text">_x000D_
_x000D_
<button onclick="do_check()">check</button>
_x000D_