NATO is an organisation and people want to join it - and it has more countries than the EU.
Let me guess: NATO doesn't count because...
Sorry, the EU does not have any special mythical status that does not apply to other organisations, unless you want to play word games so it's the only one that even qualifies.
Apples, Oranges etc once again. Of course NATO is a completely different kind of organization from the EU.
The Catholic Church has more members than NATO, too, but it's a completely nonsensical comparison.
The EU doesn't have some mythical status that doesn't apply to any other organization, it just has a very specific status in political science that it's the most successful example of: Supranationalism.
Anyways, why are we doing this silly phallus size competition in the first place? Can't we just accept that the EU is a major player on the world stage and that people look up to it?