In reply to Gtob:
You can find quieter areas in both Picos and Pyrenees, though August is as busy as it gets for both.
If Picos, stay away from the central massif. The western massif is gorgeous and much quieter.
As others said above, in Pyrenees stay away from honeypot areas such as Ordesa, Monte perdido, Aneto, Aigues Tortes etc. You could try the bit where the Vasque Pyrenees turn into the Aragon Pyrenees.
My info is all about 20 years old, so take everything with massive amounts of salt!