Go to Settings>Accounts, and select Dropbox and Facebook. Are there options to sync the Gallery? If so, make sure it's checked on. For Picasa, go to Settings>Accounts-Google>[your Google account], and make sure Gallery or Picasa is checked on. It might also be in the Samsung account menu.
Just to be clear, has it always been like this on your S6 Edge, or were you able to see your Facebook, Dropbox, and Picasa pics at some point in the past on the same phone? You're not comparing it directly to the Note 4, are you?