Having lived in Spain for many years, Cafe Iberico is by far the most authentic in the city. As for the noise, that makes it all the more authentic for me. They also have a deli that you can take out some of the great food including sausages and cheeses to be enjoyed later at home.
Arco de Cuchilleros should be avoided, in my opinion. Cafe Babareeba is very Americanized. The two times I have been there, I could not find someone who could even understand Spanish to take our order.