Feature #1 is security. In BlackBerry there are separate chipsets for voice calls and running apps.
Blackberry is able to encrypt every channel of communication including voice calls, Internet connection and individual emails. That will never happen in Android because GMail need your email to be transferred unencrypted. Otherwise they will have no idea what AD to show you.
If you loose your device, it could be erased remotely.
This product is designed for business people. So all the basic functionality is superior. You always can hear your party well due to high quality of hardware components.
BlackBerry Hub. I have never seen anything better for texting. It consolidate your email, SMS, messenger and social accounts.
Messaging is not the only type of collaboration people need for doing business. All the address books, calendars, etc. could be syncronized with wide range of corporate server software.
VPN could be established to a wide variety of routers. You can get remote access to any resource in your office.
You can still run Android apps in a build-in jail.
You can connect your BlackBerry to a TV-set or external monitor through HDMI and show presentation at client’s office. Or just a slideshow or movie to your parents. Same content could be shared over network using DLNA protocol. Your smartphone is your media-server. Those features are not available in iPhone because they want you to purchase other Apple products.
Thus BlackBerry takes best features from both Android and iOS, but it doesn’t have strings attached.