Total Recommendations: 4
Both of these anime have incredibly intelligent protagonists that use their brains rather than strength to discretely manipulate their respective new worlds to their choosing. Both main characters are ten steps ahead in their respective games and the psychological warfare is amazing in both, Log Horizon however having a slow start.
They're both about the main characters going back in time in some way to correct there past or change there future. They both have drama but Again is a lot more lighthearted and less morbid.
Both these series have romance elements and an interesting story so far. They also both center around popularity and other people's impressions of the main character. The main characters are very self conscious.
These series both have very detailed fantasy worlds that pull you in. They're also the best ongoing shounen manga right now. One piece is still better, it's got a lot more content which helps with character development and world building.