Transferring data and apps

iPhone to iPhone, there are three ways,

1. Quick Transfer --> Use QuickStart to transfer data to a new iPhone, iPad or iPod ...
2. Restore from iCloud Backup --> Restore or set up your device from an iCloud backup - Apple ...
3. Restore from iTunes backup --> Restore your iPhone, iPad, or iPod touch in iTunes on PC ...

After the transfer, whichever of the three processes you use, stay connected to the internet and continue using the iPhone. Depending on the internet speed all apps will get downloaded from the App Store automatically. Apps don't transfer from iPhone to iPhone, only the app data along with app links to the App Store gets transferred.