T Y Lin discusses some neat aspects of bridge design that touch on this in his oral memoirs. 
IIRC, cable-stayed bridges have the advantage of being able to be cantilevered from the tower out during construction. Their disadvantage of compressive load on the deck goes nicely with prestressed concrete's strength.
The whole memoir is really good.
> Lin: This was all concrete. Except the cables. See, cable bridges are really prestressed concrete. To tighten the cables against the concrete, but put the cables outside; for ordinary beam, the cables are inside. When the bridge gets too long it is cheaper to put cables outside, so it s really a type of prestressed concrete bridge. They call it cable-stayed bridge. It's post-tensioned concrete. So, okay.