Data transfer from one phone to another becomes easily for now due to increase number of apps. But unlike contacts/photos/music, which can be backed up and restored through cloud services, text messages is much different as you can transfer them in normal ways. You have to export them in xml and import the file on the new phone. The most comfortable way for sms transfer is this: http://www.androidphonesoft.com/resources/transfer-text-messages-from-android-to-iphone.html
The above demo is for iOS and Android, it also works for Windows and Blackberry phones.