As the others have indicated text messages can be moved to your new iPhone. Here are the details on the type of messages covered by an iCloud backup or iTunes backup: iMessage, text (SMS), and MMS messages (requires the SIM card that was in use during backup).
Also as willmtaylor indicated, turning on encryption for your iTunes backup will also save your passwords ( including Wifi ), health data and App data, Contacts, Camera roll, etc...
Dave