Why can't I see my historical sleep data on my new smart phone? Nothing else has changed. I used to be able to see sleep cycle, etc on mobile app.

Do you see other historic data like your training history? 

Unless you see some of the historical data as e7andy asked, you are not logged into the same account as on the old phone. Sign out (Garmin Connect Mobile menu » Settings » Sign Out), and then sign back in with your original credentials. You may need to check your mailbox archive, to see what email address you have been using originally.