Hi, there is just one taxi company, they are all the same prices.
I can only recommend one thing if you pick a cab. If you want to go to the station, airport, or places like this, do not tell the driver, look at google maps and ask for a direction near by, they got a 2€ plus for those. Also do not suggest to hurry, another 2€ plus, also extra bags, got plus per each...
Btw Barcelona have a great public transport, awesome subway. But the best of all is taking the regular train for cross the city, check Sants Estació - Clot, there is a line that crosses the city stright line, you can be from one side to another in less than 10 min ( same traject with sub its about 45 min ).
If you finally use the public transport check the bonuses, single tickets are really expensive, the t-10 its still expensive and its 50% less per traject than the single ticket. If you stay for one month at least I would recommend the 50/30 ( 50 uses in 30 days ), its the most common for +25 years old I think.
Hope I could help you someway.