I can only speak for the Hostel Conchita I and II. They are actually two seperate hostels, Hostel Conchita I is owned by a woman named Ines, and that is located at Calle Preciados, number 33, second floor. (Really the third floor by American standards.) No elevator.
Hostel Conchita II is owned by the daughter of Ines, Ana. Ana is really nice and friendly. Conchita II is located on Campoamanes, 10, 4th Floor (there is an elevator.)
Both Conchita Hostels have small refrigators in the room, which is awesome. For us, that was a big draw, since we are in Madrid for a long time and being able to keep food on hand for dinner saves us lots of money. Both hostels are pretty small, with only a few rooms, so book ahead.
Conchita I is a bit closer to the center, very close to Gran Via and Sol, but it is also considerably louder, as it is on a busy street. Conchita II is on a much quieter street. I also thought that Ana, the daughter, was significantly nicer than her mother Ines.
At Conchita II, we have had to ask for toilet paper repeatedly, since Ines has not left us a new roll. She also said we could receive phone calls between the hours of noon and 11, but she is gone a lot, and you can´t receive calls when she isn´t home.
Lets see, what else...both are reasonably priced, we paid 16.50 each at Conchita II for a double, and 16 each person at Conchita I for a triple. Not the best deal in town, but the private bathroom and refrigerator are nice.
All in all, I recommend Conchita II over Conchita I. If you have any more questions, feel free to email me.