You can transfer your account between devices, but only if they are both the same operating system: iOS to iOS or Android to Android. 

When you log into Bricks n Balls, go to the SETTINGS menu by tapping the rotor icon in the upper left corner of the screen. From there, look for the Account Transfer link. Tap this link first: 

 

From there, you'll be given instructions on what to do. First, you'll want to get the code from your OLD DEVICE from the orange button. Then you'll want to go to your NEW DEVICE and enter the code by tapping the green button and entering it there: