Sounds like you're connecting the device directly to the audio system. With a radio transmitter, you're broadcasting on an fm band that the car picks up via the fm tuner.
Of course if the person is willing to attach something to the car audio as you have, that's the best!
I'm not sure what you were suggesting before, then, when saying that a bluetooth transmitter is worse than radio... ah unless you were talking about some kind of device => bluetooth => fm => autoradio contraption?
I didn't think about that, yeah, but the OP said they had an AUX input, so quality should be good with a (even cheap) bluetooth adapter on that.
Of course if the person is willing to attach something to the car audio as you have, that's the best!