Great question this. I think it’s open to different interpretations. Both raised the standard of modern football it’s insane how good they were.
Football / Soccer / Calcio / Futebol / Fußball
Your title and body state two different things: 'better' and 'more successful'. It's hard to argue with Real's CL wins in terms of most successful. but the least random variance influenced data points of which team was better than the other are the yearly La Liga standings. And in that, Barcelona dominated Real.
Madrid doesn’t have much other than UCLs if they won 1/2 more leagues they would have won easily imo
2008-2014 Barcelona was so dominant that no team would actually go up and beat them. Most of their losses came from insane games with 0.1XG team winning, even bigger teams. Of course there are exceptions but they are so few and far between. That Xavi Iniesta Messi Busquets Alves core was the most dominant side we have seen in the recent times. At one point they were trashing RM left and right at classicos too. Real would get wins but Barcelona wins were proper demolitions with 4-5 goals. Add to all that that REFs were very biased towards them, yep, they were the most dominant and successful team of the era.
Are we including the Negreira factor in the equation?