$.fn.isEqual = function($otherSet) {
  if (this === $otherSet) return true;
  if (this.length != $otherSet.length) return false;
  var ret = true;
  this.each(function(idx) { 
    if (this !== $otherSet[idx]) {
       ret = false; return false;
    }
  });
  return ret;
};

var a=$('#start > div:last-child');
var b=$('#start > div.live')[0];

console.log($(b).isEqual(a));

Selectors are ARRAYs ... so you should do something like this 
<div></div>
$('div.a')[0] == $('div#a')[0]

or use the bellow method

JQuery Compare Selectors

jQuery