Ajax na mão vs. Ajax com JQuery.

finaliza-ajax-com-jquery.js

function finaliza(id){
    $.post("finalizaTarefa", {"id": id}, function(){
       $("#tarefa_"+id).html("Finalizado"); 
    });
}

finaliza-ajax-na-mao.js

function finaliza(id){
    var xmlhttp;
    if(window.XMLHttpRequest) {
        xmlhttp = new XMLHttpRequest();
    } else { //IE 5 e 6
        xmlhttp = new ActiveXObject("Microsoft.XMLHTTP");
    }
    
    xmlhttp.onreadystatechange = function(){
      if(xmlhttp.readyState == 4 && xmlhttp.status == 200){
          document.getElementById("tarefa_"+id).innerHTML = "Finalizado";
      }  
    }
    
    xmlhttp.open("POST", "finalizaTarefa", true);
    
    xmlhttp.setRequestHeader("Content-type", "application/x-www-urlencoded");
    
    xmlhttp.send("id="+id);
}