Unless there is a valid reason, always book your airfare directly with the airline.
Often, fares shown on third party sites are stale and will often be adjusted when you try to book. This isn't necessarily an error on the third party, but rather how often they query the airlines for the fares available.
Booking directly with the airline often avoids this problem and if there is a flight change/cancellation, etc, it's much easier to work directly with the airline then through a third party.