You can just substract two Dates from one another, the result will be the difference in milliseconds.
From the Mozilla Developer Network:
// using static methods
var start = Date.now();
// the event you'd like to time goes here:
doSomethingForALongTime();
var end = Date.now();
var elapsed = end - start; // time in milliseconds
Since Date has a constructor that accepts milliseconds as an argument, you can re-convert this to a Date by just doing
var difference = new Date(elapsed);
//If you really want the hours/minutes,
//Date has functions for that too:
var diff_hours = difference.getHours();
var diff_mins = difference.getMinutes();