The dumbbell row is a unilateral movement meaning it works each lat independently. You are then able to fix any muscle imbalances. Another key note is that the dumbbell row is great for hypertrophy training. You are able to work the muscle with a lot of reps because your weight is supported taking the pressure off your lower back.
The barbell row is mainly a strength movement but can also be used as a hypertrophy movement as well. There are different ways to attack the back muscles with the barbell row based on your degree of bend in your hips! Your lower back and core stabilizes the weight therefore you need to have a decently strong core to preform this movement. The barbell row incorporates your entire back therefore you can load the bar heavy to target strength training or light to moderate to target hypertrophy.