I loved them both for different reasons, I went last year for the first time. As another commenter said Madrid felt very imperial, and as you say was beautiful, clean, and walkable. Barcelona felt more arty and had a great coastal vibe to it. I would go back to either in a heartbeat!
For anyone planning a visit to Spain, I can't recommend Madrid highly enough. I wasn't sure what to expect from the city, but it might be my favorite I've ever been to. Madrid is beautiful, clean, walkable, and very welcoming. The food was all amazing and it seemed like we never had to wait for a table. I had a great time in Barcelona, but I'd recommend Madrid over Barcelona in a heartbeat.
I'd recommend Valencia in addition to Madrid. I can't say I enjoyed Barcelona that much, it felt too touristy. Valencia had a wonderful balance of tourism, low prices, food, and waterfront.
Madrid is indeed very nice. Perfect destination in early spring or late autumn as winters are very short there. Avoid in the summer as it gets stupidly hot there. One reason I like it is that it's far away from the beaches and package tourists. It's huge modern city. And there's plenty to see. I love the public parks there. There's a huge new park on top of the inner ring road which they partially covered up. Perfect place to hang out on a warm day. Also did wonders for the nearby neighborhood which are now quiet and a lot less smelly than they used to be.
There are a couple of other museums well worth visiting near El Prado. El Prado can get very busy because it's on everybody's list of things to visit. I've been there on a quiet day at some point and it's very enjoyable. But when you have to queue up for 45 minutes just to get in, it's probably a lot less nice. Thyssen-Bornemisza Museum has a pretty amazing collection and is right across the street. And down the street is the Reina Sofia, which has a nice modern art collection (think lots of Miro, Picasso, Dali, etc.).
If you have time and a car, driving around Spain is very enjoyable. I've seen most of it's larger and smaller cities over the years.
I'm Spanish, and wherever I've been in Africa, South America or Asia, everybody ask me if I support Real Madrid or FC Barcelona, soccer teams of the main cities here. And the number 1 visited museum in Madrid is not the Prado, which is one of the 5 top art museums in the World, but Real Madrid museum in their stadium.
Not much to add to the wide variety of insightful comments here, but if you'd like an American comparison, Madrid would be more NYC (busy, finance, big co's HQs, cultural offer) and Barcelona would be California (sea, weather, hotter startup scene, more laid back).
Both are awesome and whatever you choose you can't go wrong.
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