Its difficult to provide accurate data on things other than social media but here's a link. https://travel.zeelo.co/the-top-15-biggest-and-most-supported-football-teams-in-the-world/I don't understand why you dismiss Barcelona's success just because it is more recent. It's not like with City who may have won more in recent years than you guys, but have won less historically. Barca's have won more recently as well as over the whole club history. Their success is dominated by the last 15 years, but if you take out a particular decade and a half from United's history as well, you end up on the same level again if not lower.
Seems pretty arbitrary to me.
I can't vouch for this statistical accuracy mind you. But social media is also a flawed way to measure a club's popularity. I'm not on Twitter or Instagram. So does that mean I'm not a Utd fan?
Regarding the 2nd part, I'm not dismissing Barca's success because of its recency. What I'm trying to say is titles such as the biggest club are dependent on more than just trophies. A lot of other cultural factors come into play into making something more popular, and hence "bigger" for a layman. For eg Beckham was a bigger name than Iniesta, but he wasn't a better player than Iniesta. It was reasons beyond footballing metrics that made him bigger. Similarly, if we bring this debate to a club level, Man Utd have been the top dogs in England ever since the PL started getting broadcast globally, whilst Barcelona until recently( maybe even now) have been in Real's shadows. The PL is by far the most watched league in the world and its top dogs are obviously going to be highly popular all over the world. Then there was the 99 treble and the romanticization of the way it was achieved plus the story of Munich and legends like Best getting widely known. Due to these reasons, by the early 2000s Utd had amassed a global popularity that based solely on footballing metrics it shouldn't have.
Barca's popularity came on the basis of Ronaldinho and Messi and in the last few years over their public campaign as the face of Catalan independence in the face of Spanish oppression. While Utd have retained their popularity that they started gathering 25 years ago, its too early to say how Barca's popularity will withstand losing Messi. Hence, I say that based on their success in the last 15 years, it is too soon to call them as the 2nd biggest club of all time. We need to see if they maintain this popularity in the next 10-15 years.