In fanfiction, one major difference is their moral compasses. Superman is typically portrayed as a paragon of virtue, while Homelander is often morally corrupt. Superman uses his powers for the greater good, whereas Homelander is more self - serving. Also, Superman's powers are more stable and reliable. For example, his flight and strength are consistent. Homelander, in some fanfictions, may have moments of weakness or instability in his powers.
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.
It's hard to say for sure in fanfiction as different writers can create different scenarios. But generally, Superman has the advantage. His power levels are often depicted as being extremely high, like being able to move planets. Homelander is powerful in his own right, but he seems to be more limited compared to Superman. Superman's powers are also more iconic and well - defined, which might lead more fanfiction writers to have him come out on top in a battle against Homelander.