SMS Backup+, which needed for Android users. Because it takes backup copy of message and Call logs to the mobile which you provide. It is easy to install and believe reliable. If you missed your phone or flashed your phone, you can easily restore it back to your mobile.
So you will not miss any important message and call logs. It has more sync options too. To sync often it requires wifi. So it will not consume more battery. In ordinary data mode, it will wake up and sync nearly 30 mins. I hope we can change this if we need less interval.
We have more apps in Android but this is light weight and user friendly. Call logs and Messages will be in your gmail under Labels.