As for why WhatsApp specifically was such a success over competing apps, it's hard to say, but speculation is that a large part of it was due to their supporting many legacy phones.

Anyway, the main differentiator vs. SMS is simple. At the time, many carriers charged for SMS separately, even if you had a data plan. WhatsApp did not. It just used your pre-existing data plan or even Wi-Fi. You therefore didn't even have to have a data plan to use it if you could get Wi-Fi. On top of that, it was just a far more polished experience than SMS and didn't rely on MMS for pictures, etc.

This sounds trivial and it's easy to write it off, but this is why the app came to be used by half a billion people around the world instead of SMS.