Android - How to transfer apps, contacts and settings between two identical phones?

Lookout should do all, or at least most, of this for you.

(Warning: Market-speak follows)

Your mobile device is your most personal computer. It contains your personal data including contacts, photos, video, e-mail, and text messages. Backup your data and keep it safe and secure.

Whether you accidently delete data, your phone is lost, or even destroyed--your data is safe. You can restore any data with the click of a mouse. Changing devices is just as easy and your data can be transferred in seconds.

This Answer is valid for the Android 4.x.x. We will proceed with the use of ADB tool available for Android and it is not required for the Device to be Rooted at all. The answer is meant to be generalized rather than Android Device Specific.

Method using Linux System :

• Install ADB related tools from the repositories of your installed Linux Distro.
• Enable USB Debugging in Developer Options and Choose USB Storage or MTP as USB connection.
• Open Terminal in Linux and type adb start-server.
• Type adb devices. It should list the output as Serial No. and Device where Serial No. is the Device's Serial No. In case, you're getting any issue with ADB detecting the device, there are many questions at Android Stackexchange, so you may search them if you need assistance.

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Backup UserData:

• There are two options to backup the UserData (Storage where Multimedia Files, Camera Images, other stuff you store). Either by ADB collectively with Apps OR by just copy-paste.

• If your device Supports USB Storage Mount, then its easy as Linux will detect it as Removable Device and you can copy-paste the data into system.

• If only MTP is supported, download MTP specific package from your Linux repos. It will detect the device. If none works, Airdroid for Android from Playstore can help. But that would be too much to discuss here.

• Windows detects both MTP and USB Storage easily, so no need for any specific software installation.

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To backup User Apps Apk's, the App Data, Custom Settings of Android, Messages, etc.

• Open Terminal and type adb backup -f backup_file.ab -all -apk -system. This will backup only the User, System Apps and App Data with no UserData.

• If you want to backup UserData too then type adb backup -f backup_file.ab -all -apk -system -shared. backup_file.ab is the name of the backup file in your Linux system.

• It is to be mentioned that parameters like -noapk -noshared -nosystem are also available. You can check the Manual page of ADB for more commands if you want.

Note: When you enter any of the adb backup command, a window will show up in Android asking your permission to Backup or Cancel. Choose Backup; you can also select a password their but that's optional. Also make sure that the Device remains awake by changing Display settings, and don't do anything on the Android device while it makes the backup.

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To Restore the Backup:

• Connect the other device and check whether its getting detected or not on Linux,
• Type in Terminal adb restore backup_file.ab. It will show a window in Android asking to Restore or Cancel. Choose Restore and let it do the job. Restore can take a lot of time depending upon the size of backup. Besides, it might get interrupted because System Settings when restored can disrupt the Backup Window and cancel the backup. So keep trying. Reboot the device and you're good to go.

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Backup Contacts exclusively:

It is strongly advised to backup contacts through methods other than ADB.

• One option is to Sync the contacts with the Google Account in Settings and then use the same account on another device to restore.

• Other method is to open Contacts or People app (native) in Android and export the contacts to Internal/External SD card. I prefer the latter one. It creates a file with VCF format. You can open the file in another device and it will restore the contacts in it.

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I don't use Windows but there are plenty of Questions/Answers regarding how to use ADB in Windows here at Android Stackexchange, so you need not to worry at all.

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Method involving no ADB backup Commands:

• Download Helium app from Playstore and open it in Android Device.
• If you're on Linux system and ADB is able to detect your device, then you can download Chrome App Helium Backup for Linux.
• Open Helium app first on Android, connect your device to Linux, Open Helium App in Chrome now.
• If all goes fine as it should, the Android Helium app will allow you to backup directly into External/Internal SD card. Copy the Storage files into other device. Follow the same detection procedure for other device, and then you can restore the Apps easily without any commands. The backup made by helium is stored in the folder named Carbon in the Storage you selected during backup.