Well for me, the Tap & Go thing had the G4 download whatever apps were on my Nexus 6. Then I installed LG Backup on the Nexus and it brought over my call logs and text messages (minus MMS & group messages.... Seems none of them can transfer those)....
LG Backup worked for me. G3->G4 H815 ->G4 H811 - both mms and group sms.
By the way I run SMS Backup & Restore set to backup every night just in case.