Does the new Summer '16 Sandbox copy feature also copy the data ?
As per Salesforce docs
You can now create a sandbox by cloning an existing sandbox rather than using your production org as your source. Save time by populating any type of sandbox with a previously chosen set of data and metadata. (Sandbox templates, which serve a similar purpose, are available only for Full or Partial Copy sandboxes.) Sandbox-to-sandbox cloning facilitates iterative development, allowing you to freeze development in one sandbox and pick up where you left off in a new one. This feature is available in both Lightning Experience and Salesforce Classic.
So answer is yes you can move data in full copy and partial copy SB same concept we use in sandbox creation.
As per Salesforce documentation "When you clone a sandbox, all its data and metadata are copied into the new sandbox.".