WhatsApp - Its mainly one to one or Closed group conversations. One can not go to your whatsApp account and see what you discuss/share in other groups like people do in Facebook.
Facebook - Its truly "Social" networking. Like a social gathering (party), where whatever you discuss in a group will be stored (remembered) by people in a group AND also by people passing by your group (your friends). I am not sure if I am able to give correct metaphor for Facebook conversation to that of Party scene.
Now, IMHO, when we say "Social", whatever we talk is bound to be remembered by whoever has interest in that topic. Private conversations should be done in private, not on social n/w site. Like they say, best way to keep a secret is not to tell that to anyone.
So, coming back to your question - "Should I give feature to delete messages including other end too?". My opinion is -
Deleting message from your own inbox is "User's" decision for whatever reason and "User" would be responsible for the confusion/misunderstandings while reading that chat later.
It's ok to delete message from other's inbox, if it is one-to-one communication, where you can say, "I am sorry I did not mean it, or I sent it by mistake". Otherwise in a group chat, deleting certain messages from a chain of may (will) create misunderstandings.
Please explore "why" someone might want to delete a message? If by mistake he types in something, or sends message in wrong window, them make UI such that users wont commit such mistakes. May be showing group name promptly, color coding groups based on genre/social setup, alert with smart confirmations (avoiding abusive language in family groups) etc.
I would like to repeat - social networking is not for private messages. It's like shouting in public. See if by design can we minimize instances where user has to recall/delete what he has posted. If user is sure while sending something and regrets later...well..you can't rewind in social conversations. This makes social networking site truly social and not where you say something and back off later.
One more point, instead of deleting posts from other's inbox, you can have facility to mark it "non-relevant". This way, people will understand you don't stand by your earlier thoughts anymore (this is accepted as new learning can alter our beliefs). But deleting will surely cause confusion/misunderstandings.