I prefer getting stronger, so I use all the tools and movements that work my weaknesses. Dumbells are more likely to directly work the pecs and the triceps secondarily. Barbell is more likely to work the pecs and tri's equally or the tris preferentially (depending on how you do them).
There's no reason not to bounce back and forth between them or incorporate both BB and DB chest work in the same session. Just change the bench angle. Switch it up. Keep good records.