I think the only real difference is that when you use quick reply, the box is right there on the screen and you don't have to go to a different one. With new reply, it's a different screen, and the reply box is bigger, you have the smilies, etc. "Go advanced" under the Quick Reply seems to be the same as "New Reply." I may be wrong on some of this, that's just some things I've noticed. I pretty much always use the quick reply box, as I type my own tags, etc., instead of using the quote button, etc.