This is a tough question. It depends on your relationship with your friends and family.
If I had to choose between these options, I would rather choose to forget who I am. I can back this up with the following reasons
1.) If I forget who I am, I can consult my friends and family members and other people who knew me throughout my life (before I lost my memory). On the other hand, if I forgot who everyone else was, it would take a while to recollect all of those memories
2.) It would be better to forget who I am rather than forgetting the identities and personalities of my friends and family members. Especially if I had a deep connection with any of these people. It would be difficult to recreate those memories with loved ones if I forgot who they were in the first place!