Sword Art Online-based on Kirito saving the people trapped in SAO
Log Horizon-life of people who had been transported into the world of Elder Tale
The major difference I see between the two, is that SAO's world was a VR world, something which was made, and you can simply log off to return back to the original world (except SAO) on the other hand, Log Horizon is about people who were sent to DIFFERENT WORLD, with no idea how to return to their original world