One popular plot is the discovery of a common enemy that forces Superman and Homelander to team up, despite their differences. Another is a battle for supremacy in a world where both exist, with different factions taking sides. And then there's the plot where Superman tries to reform Homelander, seeing the potential for good in him.
Well, it depends on how the fanfiction is written. If it's a more 'grounded' version where Homelander's public image and mind - games play a big role, he could potentially gain an upper hand. But generally, Superman has more raw power. He can move planets, and his speed is almost limitless. Homelander is strong and has flight and heat vision too, but Superman just seems to be on a whole other level in terms of pure power.
Immortal Cultivators vs. Superpowers was a Chinese manga that was in the midst of being published. It was created by Bixue Animation. The story was about a powerful cultivator who accidentally transmigrated to the modern hero society and launched a fierce confrontation between immortal techniques and superpowers on Earth. The manga had more than 300 chapters, and the latest chapter was chapter 307. The readers can watch the manga for free through multiple online comic platforms.
The Immortal Cultivators vs. Superpowers comic was a free collection of comics created by Snowstep. The story was about a powerful person who accidentally transmigrated to the modern hero society on the cultivation continent and launched a fierce confrontation between immortal techniques and superpowers on this earth. The manga had been updated by Snowy Animation, but the specific plot and chapter information needed further reading to understand.