Coolmuster Mobile Transfer is the world's best phone to phone data transfer tool, which enables you to share contacts, SMS, photos, videos, and more between two devices (iOS and Android devices supported).
iMazing - iMazing lets you transfer music, files, messages, apps and more from any iPhone, iPad, or iPod to a computer, Mac or PC. Manage and backup your iOS device simply without iTunes. (was DiskAid)
Titanium Backup - Titanium Backup is a very old backup app that has been around since the early days of Android. In fact, it's one of the few apps that covers all versions from 1. Read more about Titanium Backup.
AnyTrans - AnyTrans is an ultimate product manager that converge your entire apple products and consolidates every access to all your content in one place including video, audios, images, messages, voice memo etc.
Super Backup & Restore - Super Backup & Restore app allows users to backup all their stuff such as pictures, videos, apps, text messages, contacts, call history, and calendar data, etc.
Wondershare MobileTrans - Wondershare MobileTrans is a 1-Click Phone to Phone Transfer for you to move data between devices with different operating systems. Your must-have phone Transfer.
Droid Transfer - Save and Print your Android Phone Messages, Manage Photos, Music and other files on your Android Phone through your PC. Android Transfer Software.