One trip from Gràcia to Barceloneta, 5km:
* Metro: 22 minutes, 1,03€ (with a T-10 card, which is the most expensive integrated transport option)
* Taxi: 15 minutes, 8-9€
* Uber: 15 minutes, 4-5€
Also, Barcelona cab drivers are known for driving you around if you look like a tourist. Uber drivers will never do that, since you rate them after the trip.