Real Madrid is a huge club, but we are the world's most famous club and also the richest club. Even with our poor performances over the last year's(last season was very good though). So I will argue we are the biggest club in the world.
That is a hard sell when both Madrid and Barcelona are more popular on social media
Also, we have only been top of the money list this last year, while Madrid has been top for 11 years prior (since 2005). Currency fluctuation and sponsorship renewals might see that change again soon.
We have been missing on the biggest stage in recent years while Madrid as won 3 of the last 4 CLs.
Madrid have a more star studded team with CR7 being one of the top 2 most popular players and winner of 3 of the last 4 Ballon d'Or.
Madrid have repeatedly signed top players from most other teams except maybe barcelona and atletico, and have enough pull that they rank top destination for most of the best players and talents e.g. current Mbappe saga.
If any club can claim to be the biggest in the world, Madrid have a better claim than us.