Btooom!, Log Horizon Recommendations
The environment that both series take place in has a similar concept but with different circumstances.
As for our main characters, they are stuck in an isolated area from the outside world where they must survive. Btooom! takes more of a serious tone, while Log Horizon is much more lighthearted. However, there are many mechanics behind both series that are explored relating to their circumstances.
The main male protagonists are also gamers with experience in the gaming world.
Rather than being trapped in a gaming world, the characters are abandoned on a deserted island to play the game for real.
Both series have certain natural laws that are based in or off of a videogame.
Both also have a romantic sub plot.
Both have great main/side character development.
In both animes they suddenly get stuck in a game.
Both anime are about people getting tuck in familiar situations one a game, the other a game like setting, the main characters always come through, and are strategic.
Virtual World / Game World
Both anime take place in a virtual world which is similar to a game the characters played in the real world.