comparing jQuery objects

Following on from bobince, instead of using wrapper[0] use the proper get(0) method to return the first element stored in your jQuery object.

var focused = null;  
$(':input').focus( function() {  
   focused = $(this);  
   compare($(this)); 
   //Compare them...trivial but will return true despite being different jQuery objects.
}).blur( function() {           
   focused = null; 
});

function compare(element) {
   if (element.get(0) === focused.get(0)) {
      alert('The same');
   }
}

You can't make the comparison on the jQuery wrapper, but you can make it on the underlying DOM Node. Lose a few dollars and you're fine:

.focus(function(){
    var that= this;
    $openMenus.each(function(){
        if (this!==that){ 
            [do something]
        }
    });
})

(or use eg. wrapper[0] to get the DOM Node from a single-item jQuery wrapper.)

(I used === for the comparison because it's usually best, but it would work with == too in this case.)