Telegram:
Not owned by Facebook.
Open API meaning that anyone can write a client for it. Which means you don't really have to worry about Whatsapp pulling support for your device. It also allows for some interesting control applications. Some people have written apps that they use for remote monitoring of hardware and such.
Messages seem to be delivered faster.
Proper desktop and tablet clients.
Stickers (my mom seems to spend her life looking for cat stickers).
Supports calls between desktop and phone.
Has self messaging (very useful if you want to easily transfer small things between devices).
Group bots are very useful as well.
Secret chats are also very useful, especially self destructing ones. If I have to share a pin or a password with someone, I setup a self-destructing session.
Whatsapp:
You can use it to tell people about Telegram.
My immediate social network consists of friends and family, and almost everyone is on Telegram.