WhatsApp came to Europe at a time when there was a strong need to replace badly overpriced SMS. In the US most telco's offered subscriptions with free, unlimited SMS and WhatsApp didn't provide any immediate benefit. Facebook Messenger came later, but had the ability to send messages without contact information, giving people in the US a reason to adopt it.
By now, most people in Europe also have Messenger, but still mainly use WhatsApp (slightly generalising). I think that primarily comes down to WhatsApp being a much better messenging app. It's quick, reliable, easy to use, power-efficient, small, well-integrated into the OS, secure, and most importantly: media sharing just works.
I think this theory is quite solid. For some reason denmark has always (or at least for a very long time) had unlimited sms/mms in most subscriptions.
We also have a low WhatsApp adoption rate. Lately fb-messenger is winning territority (and so is snapchat, but for other reasons), since it offers good group chat on top of a service that already covers north of 80% of the entire population.
In Germany, the mobile plans are extremely stingy with minutes, SMS and data for some reason. I personally use Telegram (trying to convert friends to it), WhatsApp (everyone is on it), FB Messenger (everyone is there), iMessage occasionally, Skype for Voip, and I've stopped using Viber as no one seems to use it anymore (it was extremely popular about 2-3 years ago though).
By now, most people in Europe also have Messenger, but still mainly use WhatsApp (slightly generalising). I think that primarily comes down to WhatsApp being a much better messenging app. It's quick, reliable, easy to use, power-efficient, small, well-integrated into the OS, secure, and most importantly: media sharing just works.