The iTunes way still remains the most simple and error free as long as the devices are detected. Install iTunes, then connect the first phone and click it. Go to Back up Now and create the backup. It might take a while based on how much content you have stored. Once it's completes, connect the new phone and click it then go to Restore from backup. Choose the previously made backup and wait for restore procedure to complete. Reboot the phone and that's it.