I'm flying the 720. What's being talked about here at 500m and 1000m is two different effective ranges. At 500m most people are losing FPV or First Person View which is the video feed to the phone. This is somewhat variable between phones and not all are created equal. I had decided to use a spare cell phone for drone control, but found the connection range was lesser than my daily service model.
At 1000m the controller is losing the connection to the drone for greater than six seconds causing one of many RTH or Return To Home conditions to activate. Obviously this is dependent on several factors such as atmospheric conditions, operating altitude, and line of sight obstructions. The range is not generally dependent on use of Tapfly or manual control inputs. I personally like the Tapfly as you can be more certain of travel direction despite any heading deviation due to winds encountered on the route. Also pay attention to altitude selection as it can be affected by sudden wind sheer.
Lastly since we are discussing range, avoid flying below 15m/49 ft as the battery is expended below three bars when the 100m/30m limits are in place(yellow colour status background) and the drone flashes red. If the battery level goes critical while the drone is within 15m and under 15m altitude, the drone will automatically land wherever it is as opposed to coming back to the safe home/takeoff area. This can be quite colourful when there are trees or water about. You will have forward/backward, side motion, and rotation control, to affect the final position, but the drone will be on an unstoppable descent during this short time period from somewhat less than 15m/49ft. If you are further away than 15m, the drone will climb to 15m or maintain higher altitude and return to home before descending which is more favourable.