As measured by the IOS app store.
To resolve, I will first look at the Apple's list of top iphone apps. If that is unavailable, I will look at number of downloads. If that too is unavailable, I will consult the number of ratings. If all three of those are no longer public, or if the app store isn't a thing anymore, I will consult the community and my best judgement on what the biggest app is.
The prospect of sex or romance must be the primary marketing for these apps. Chatgpt and Character.AI do not count as romance apps, nor do Facebook and Whatsapp. Hinger, Tindr and Grindr are human romance apps. Nomi and Candy AI are AI romance apps. The biggest app does not necessarily have to one of the apps I named, but these examples should elucidate the boundaries of a "romance app".