Contract company or direct to the airline... Is one better than the other?

[Capt737AA]

In my beginning quest to gather info on flying outside the US, I'm getting a read that sometimes one can get more favorable terms either using the Contract company like Parc or Rishworth vs just applying directly to the airline.

Can someone explain to me how this works and if one path is generally considered more "lucrative" than the other?

Thanks for the assistance.

Pat