It really depends if you booked just a hotel or a hotel + flight.
My biggest issue with using a third party site for Disney is that for travel within North America whenever possible I only fly Southwest. Free 2 bags + carry on + personal item is hard to beat, and I've never had a service issue while flying them (and I constantly hear horror stories about United). But because Hotwire, Hipmunk, and Orbitz don't have flights with them I rarely, if ever use them.
If you are heavy packers I would double check how much each bag will cost you if you fly through the Orbitz airline. If the airline charges $50 per bag and there are 4 of you, you easily lose half the savings you got from booking through Orbitz. You'd need to compare how much you saved against the rate per flight Southwest offers, but from what I've been told they're not usually that different.
For me, it's not worth the hassle of the potential service issues + luggage costs.
If it's just the hotel, I booked our hotel + tickets through a Disney package and our flight directly through Southwest. If we had been staying offsite and not at a Hilton hotel I would have possibly used Hotwire just for the hotel (though the hotel I had experience with was unavailable), but due to the price point for the package (tickets + hotel) - the amount we would have saved (going through the Ramada website) would have been negligible to us at around $200/ea ($50 a day). It was well worth it to stay onsite.