The Conclusion:
There is no concrete conclusion to this question because it must depend on your exercise needs. That being said there are definitely times where dumbbells will fit your needs better than barbells and vice a versa. For example if your lifting at home with no spotter, dumbbells are definitely your answer, same if you're looking to balance out unequal body parts. But if you’re looking to build as much strength as possible then you need to go with barbell training.
The knowledge you need to take away from all this is that the best well rounded workout program for you will probably consist of a well thought out combination of barbell and dumbbell training.