It depends on personal preference. If you like to see the story visually and enjoy fast - paced action and great animation, the anime might be better for you. The anime has some really cool battle scenes and the character designs are appealing.
It depends. Sometimes the manga can delve deeper into details and offer additional plot points that weren't shown in the anime. However, the core storylines often remain similar.
One major difference is the level of world - building. The novel is able to build the world of Log Horizon more comprehensively. It can describe the different regions, cultures, and races in great detail. The anime, while it does a good job of showing the main areas, can't cover as much ground as the novel. Additionally, the dialogue in the novel can be more complex and nuanced, as it doesn't have to rely on voice acting and visual cues to get the point across like the anime does.
Yes, the Log Horizon light novel does continue past the events covered in the anime. There are many new storylines and developments waiting for you in the novels.