Most of the data transfer software including Samsung Share will transfer most of your data to your new phone but I just noticed today that the whats app messages were not transferred even when I selected everything while transferring data from note 2 to note 3.
Steps to transfer whats app messages from old android phone to new android phone:
1) On your old phone, Go to whatsapp, press menu button, go to settings==>chat settings ==>Backup conversations
2) Connect your old android phone to the computer using the data cable.
3) Go to your phone and copy WhatsApp folder on your computer.
4) Disconnect your old phone from the computer and connect your new phone to the computer.
5) Copy the WhatsApp folder to your new android phone from the computer.
6) Install Whats App android app on your new phone.
7) Verify your number.
8) After verification, the Whats App application will confirm if you would like to restore data from the back. Select to Restore.
9) The process will run, it takes a few minutes depending on how huge the data is.
10. Job Done. All WhatsApp data including chat conversations, images, videos etc has been transferred to your new android phone.
Some Important Tips:
This method only works with Android phones. This means that both old and new phones should be Android phones.
If you have already installed WhatsApp on your new phone, uninstall the WhatsApp application on your new android phone, copy the data on your new phone, then install the Whats App application and follow the on screen instructions.
Please do let me know if you encounter any issues.