Barbel row is a tougher thing to do as you must stabalise your body through the pelvis. The DB row typically allows you to concentrate more on the pull with the lat because you are braced on the bench with the "non-working" arm.
I prefer the barbel row because it is a more basic, compound, closed chain exercise - but do love to show off occasionally with the dumbells - lifting the 165's for reps...