I've done both a few times. The Pyrenees is your relentless Alpine switchbacks, one hairpin after the other plus long sweepers in between. Absolutely fantastic riding and one of the few places where I've turned back and did a stretch of road again because it was so good. Besides the scenery, which is breathtaking, in terms of things to see/do, not a lot. For example I thought Andorra was tacky, uninteresting and full of the sort of people I go on holiday to get away from. The Picos also have brilliant roads but are a bit more varied and have lots of surprises round every corner; also a lot more Spanish than the Pyrenees (obviously!). Probably not quite as spectacular riding but still very, very good.
Either is fantastic though ...