Yes, most notably! I don't think the second one will work (and if it does, not very portably). The first one should be OK.
// HTML:
<input id="theId" value="test" onclick="doSomething(this)" />
// JavaScript:
function(elem){
var value = elem.value;
var id = elem.id;
...
}
This should also work.
Update: the question was edited. Both of the solutions are now equivalent.