Everyone brings up a great points, especially about have 2 pulling movements for each pushing movement.
But, back to your main question about barbell or dumbbell for chest development. When performing chest exercises with dumbbells you are able to use a bigger range of motion allowing for a greater stretch, you also have to recruit more muscle fibers in order to stabilize the dumbbells which will aid in muscle growth (the more motor units you activate during a lift the more you prime your body for muscle growth).
Barbell Bench on the other hand - is more stable, you are able to use a heavier load and makes it easier to emphasize the mechanical stress of the eccentric portion of the lift.
Also, technique plays a huge role when bench pressing. Many benchers have horrible form and put the majority of the stress on their anterior delts rather than using their chest.
My thoughts are kind of all over the place, i know, but just wanted to get some simple things out there.