An advantage of barbells is that your work out will be much quicker, because you don't spend time changing the plates on the barbell. I like the convenience of just grabbing what I need. This is particularly so if you change the weight between sets of the same exercise and if you choose to speed things up more by switching back and forth between exercises. Today, e.g., I did three sets each of biceps curls and triceps kickbacks in the following order:
curls 10 lbs
kickbacks 10 lbs.
curls 20 lbs
kickbacks 15 lbs
curls 20 lbs
kickbacks 20 lbs
I start with lower weight in the first set to warm up the muscle. I alternate the exercises in order to save the minute or two of rest I would otherwise do between each set of the same exercise.
When I alternate, I try to do so between exercises of the opposing muscle groups. E.g. chest/back, deltoid/traps, biceps/triceps.
On the other hand, sometimes, to keep yourself interested in working out, you need to change things, e.g. the exercises, the routines. So switching back and forth between the barbells and the dumdbells may be one way to keep out of a rut, if that ever happens to you.
Good luck.