Power and training. Since Goku is known for his power - seeking, his brother in fanfics often has a similar drive. They might train in unique ways or discover new forms of power.
Loki would also be a difficult adversary. He's very cunning and could use his tricks and illusions to try and outwit Goku. Goku would need to rely on his senses and ki to see through Loki's deceptions.
Vegeta could be a great rival. He might see Goku's new position as God of Destruction as another thing Goku has achieved that he hasn't. This could fuel their competitive nature even more.
In general, it's a bit of a toss-up. The strength of Manga Goku and Anime Goku can vary depending on the specific arcs and battles. Sometimes, it might seem like one is stronger in a particular situation, but that could change in another.
A really interesting 'brother of Goku fanfic' is one where the brother was sent to a different planet. The story details his journey to find his way back to Earth and reunite with Goku, while also facing many powerful enemies along the way.
One possible plot could be that Naruto, as Goku's brother, has to learn the ways of ki while also maintaining his ninja skills. Maybe they team up to fight a common enemy that threatens both the ninja world and the Dragon Ball universe.
Well, Vegeta would be a likely character. He might be initially suspicious of the female Goku. Maybe he thinks she's a threat or just can't believe there's another Goku - like being. He could be there to add some comical moments as he tries to understand the situation.
Chi - Chi might be one of the first to support them. Despite her past relationship with Goku, she could see how happy Goku is with Android 18 and decides to be happy for them. Also, Krillin would likely support the marriage. He has a deep friendship with both Goku and Android 18. He knows Android 18 well and trusts Goku, so he would be all for their union.
It could be a female Namekian. Since Namekians are also very strong and have their own unique culture, a female Namekian could catch Goku's eye. They might bond over their mutual respect for life and their experiences with fighting powerful foes.