damola, if you honestly believe what you read that Arsenal have more fans and are a bigger brand World wide than Liverpool Football Club I don't know what anyone, let alone myself, can tell you.
Fan wise, there's only the two Spanish giants and maybe Celtic and Rangers that compare to Liverpool and even more so Utd on a World wide basis.
This isn't the best example given its a traditional stronghold, but as an example I was in Belfast over the weekend. And I saw loads of Liverpool and Utd shirts. And even more Rangers and Celtic shirts. With a couple of Chelsea. And nothing else. And I can guarantee wherever I go in the World, the main two clubs anyone wants to talk about are Liverpool and Utd. Arsenal barely register in Europe down to having little to no European history. You can mock history as much as you like, and try push Arsenal down to being a financial player today; but you honestly are nothing of a name compared to the North West's big two.
Feel free to argue the contrary. Everyone that knows knows. And like I said, there's little gonna' change your sadly ill informed mind.
You want to travel around the World and test your theory out. You'll be surprised at the outcome.