In terms of cost versus a taxi, it comes out about the same, the one disadvantage being that taxis come to you - you don't have to search around for one. Also, you can't sign out from the car outside city limits/their service zone; you're still on the meter until you bring it back. That said, as an alternative to car rental, Traficar is quite a wonder. You can rent a vehicle for as long as you want at only 4.99 zł to start and then 1.89 zł per kilometer, or for 24 hours for only 69 zł a day and then .99 zł per kilometer. And you have none of the common shenanigans of a car rental; plus you don't have to pay for gas. You can also drive and drop it off in another Polish city like Łódź, Kraków, Wrocław, Poznań, Gdańsk, Szczecin or Katowice where Traficar operates. As such, this is a great option for day and weekend trips, as well as big shopping trips, or simply picking up friends at the airport.
One important thing to note is that you need to have a valid driver's license that is recognised in PL. As with regular car rental, citizens from countries that didn't ratify the Vienna Convention on Road Traffic cannot drive on their home licenses; unfortunately this includes Americans, Australians and the Chinese, among others, for whom an International Driver's License is required.