Originally Posted by Infiniti7
Once you delete an App off your phone the data is gone. It could be saved in a back up if you sync'd your phone... also if it had game center data it will ask you if you want to keep it or not.
My guess is that game data does not transfer from a free app to a paid one, unless its something like words with friends, where the data of your game is saved on a server and can be sent to the new app. If you're playing something like N.O.V.A. you probably won't get the free app data transferred to the paid one.
The difference between paid games and free games is usually the amount of ads that are put onto the free ones. Sometimes devs will put out a free version, but they still make money off of the ads that are displayed during the game, so giving it out for free pays for itself. And if you really like the game and find the ads annoying, you can choose to buy it with no ads.
The only other way to transfer saved game data from free to paid (assuming its not sever based) would probably be though SHH, and you manually transfer the files.
hope your question is answered