Maybe the answer is much simpler. Madrid is just special. A level above Barca. Well more accurately, a few more levels above Barca.
Madrid have won much more, but as someone who supports neither club, they have never had a team like Pep's 2009 or 2011 teams (not even the teams in the 50s). Furthermore, I have rarely been impressed by Real post 2009, despite winning a lot. They often win trophies without being the best team or playing the best football, which is a charge you cannot level at Barca. Barca destroyed their opposition in the 2009, 2011 and 2015 CL Finals. The only CL Final Real convinced in was 2017. 2014, 2016, 2018, 2022, and 2024 they were arguably the inferior team, but they get over the line - there's zero romance or purity in that.
More accurate to say Madrid have a relentless but hollow ability to win. Barca win less, but they do it with romance and style and artistry, and it is more memorable when Barca win than when Real Madrid win.
The fact is no Real Madrid team in history can beat Barca 2011. Real Madrid can win all they like while being outplayed, but I am a big believer in the beauty of football. Netherlands lost the 1974 World Cup final to West Germany, Hungary lost the 1954 final to the West Germans - but I consider the losing team better and superior to watch.
This is a very long-winded way of saying Real Madrid win, but they don't often leave you thinking 'wow'. Barca do leave you thinking 'wow'.
You say Madrid are special? I think it's the other way around - Barca are special as they have a philosophy and way of playing in their heyday that is football from our dreams. Barca and Pep have totally revolutionised and influenced modern football. Real Madrid don't have that. They just win while rarely convincing, it's fucking cheap and shite to watch. Real are the biggest club in the world, but there's something very hollow about them that is hard to explain.