Kirito from SAO might initially be a bit skeptical of the more complex systems in Log Horizon. He's used to a more straightforward 'fight and level up' kind of world. But he could gradually come to respect Shiroe's intelligence and leadership in understanding the game world on a deeper level. Asuna, on the other hand, could bond with some of the female characters in Log Horizon over the shared experience of being in a virtual world and having to deal with various challenges.
The characters would likely start by testing each other's abilities. The SAO players might show off their combat skills, while the Log Horizon players could demonstrate their knowledge of in - game economies and politics. There could be some friendly rivalries at first. For instance, Klein from SAO might challenge some of the Log Horizon guilds to a friendly battle to see how they stack up. But as the story progresses, they would realize they need to work together, especially if there are threats that neither group could face alone.
The interactions could also be based on cultural differences within the game worlds. SAO has a more individualistic culture where players often strive for personal glory. Log Horizon has a more community - based culture. This could lead to some interesting conflicts and reconciliations. For example, some SAO players might see the Log Horizon way of doing things as too slow or bureaucratic, while the Log Horizon players might think the SAO players are too reckless. Through various events, they would learn to appreciate each other's values.