Almost everybody may know what BBM is, but if you don't it stands for (Blackberry Messenger), and it is just that, a messaging platform designed for Blackberry smartphones, and until 2010 (give or take) it was the most used messaging platform in the world.
When iPhones and Android phones started to be more numerous than Blackberry ones, users needed to stay in touch and BBM does not work on other platforms beside Blackberry. WhatsApp was the first to fill that gap, but now there are a lot of others.
Now, when some months ago Blackberry announced that BBM was going to be released for iOS and Android "this summer", a lot of people started to say it was just too late, but for lots of others is something they were waiting for years.
BBM until now has been based on PIN IDs in order to connect people, you have a unique PIN associated to your phone, that you exchange with people and they become part of your list of contacts. To be available in other platforms they are switching from PIN IDs, to Blackberry IDs (based on emails). On the other side WhatsApp is thought to be a SMS replacement, as such, it is based on your phone number. Any one who knows or "guess" your phone number and contact you via WhatsApp (provided you have it installed), just the same way anyone who knows your number may text you.
This difference is what is going to get users for each one of them. On one hand the WhatsApp approach is easier, no IDs exchange hassle, on the other side there is less privacy, as anyone can contact you, even if you don't want it (you can block someone). Some people will prefer one or the other method, and that will for sure define which one to use, for those people.
Another important feature (at least by the time of this writing), is that BBM lets you know when the other side has read your message, WhatsApp only displays info about the message being delivered to the phone or not, but you never know if the message has been seen or if it is just waiting in an unattended phone. Once again, there are people who like this and who don't. You would like to know when your message has been read, but sometimes you do not want the other side to know you have read his/her message, it goes against your privacy (according to some).
BBM is more feature rich that WhatsApp, it lets you talk for free, and now also do video chats when on WiFi networks, WhatsApp does not let you do that, but it seems those features will not be available from the day 1 in Android and iOS platforms, also the screen sharer feature is a really nice one, that is not going to be present from the first day, but yes later.
Maybe the most important thing to consider is that where your contacts are, for most of people is some countries the answer to that is WhatsApp, but there are still a lot of regions where BBM is widely used. In fact a lot of people still use Blackberries just because of BBM, and as soon as it will be available on other platforms they will switch to that platform. That is something that some expert have analysed and some think is not a good idea from Blackberry to release BBM as a cross-platform application, because they will lose users. Now, BBM will require Android 4.0 and up, and iOS 6 or later, then it will work on medium to high end phones, on Android and iOS platforms, on Blackberries it works on very cheap terminals running OS 5, which most teenagers use in Latin and Asian countries, as they can only afford those.
As you can see, there are too many variables, and a lot more opinions based on those variables, you may have your own, but only time will tell, for now, the only thing we can do is to wait until Blackberry (former RIM) release BBM for Android and iOS, the sooner the better, I am looking forward for it.