In general, I think it's a much better idea to book directly through the airline for one simple reason. IF you have any change in plans, you only have the airline's policies to deal with. If you book through any third-party site, you have both the airline policies, and the third-party site's policies to contend with. And the third-party policies are always going to be more restrictive than the airline.
In addition, on the airline site you will usually find many more flight options -- all at the low price. So you usually will pay the same, but have many more choices of flight times, connections, etc, etc.
For those reasons, I research flight prices on travel sites like Travelocity -- but I BUY my tickets directly from the airline.