If you work for a company, most likely you will have health insurance through your company. Does this mean that you will do better going to a private doctor?
Surprisingly, not. The best doctors tend to be better in the public system, since the benefits are better (job security as well) and it's much harder to get in. If you have enchufe with a doctor in the public system, even better :) I've been pretty disappointed with the private doctors in general, especially the ones that some companies can send to your house. They are usually straight from Cuba with a tendancy to prescribe antibiotics for everything. (What is it with Spain and over-the-counter antibiotics? They laughed at me when I asked for a prescription for an antibiotic. Just go buy it! All the bacteria here must be immune to the stuff by now.)
However, they tend to want to get the appointment over with quickly in order to stay on schedule (I love how they give you an appointment at 12:37 exactly). If you want someone to listen to your sob-story, then go to a private doctor.
Test results in the public system are a bit of a pain. Doing the test is usually pretty fast, but then you might have to wait months (if it's non-life threatening) before you can get an appointment with the specialist to talk about the results. Also, they won't call you when your results are in, so you have to keep on top of them.