I've always done online booking because (as Bill said) it opens an hour earlier than MS. I have gotten the "expired page" sort of thing before, but typically have been pretty lucky.
But yes, if both sites are working they will see the same thing. Your best bet is to place a waitlist if you can. If some of the days are available and someone cancels a reservation that gives you all of your waitlist, the system will hold those days and process your waitlist rather than put them back in the system. If you are waiting for something to open, you may never see it if someone else has a waitlist.