1. No need to log in - WhatsApp uses your phone number and a hash of your IMEI number as credentials to log in to their app. Although this means that your account could be compromised, its ease of use is therefore unparalleled.
2. No need to authorize people to add you - this means that if you have anyone's phone number, you already have them on your contact list. If I had to choose one reason for WhatsApp getting over a 100 million users in a short time, this would be it. A lot of people find this a privacy issue (including myself), but most people just don't care.
3. Sending images and video through WhatsApp is super easy and the content is compressed.
4. WhatsApp has restricted their emoticon set - I think this makes a big difference in keeping the clutter down.
Facebook's Messenger is marketed as an IM, not as an SMS/MMS killer. Chat functionality is still seen as "bolted on" and unreliable for Facebook, so people turned to alternatives, and WhatsApp is by far the most recommended solution (peer pressure: if everyone has it, you want/need it too)
The product just isnt as good.
Also the big reason in mainland china is that Facebook is blocked there :)