In fanfictions with 'hiccup is part dragon', it completely transforms the power dynamics. Hiccup now has abilities like flying without Toothless or breathing a small amount of fire. This changes how he approaches battles and threats. He might be seen as a freak by some vikings, which leads to him having to prove himself even more. It also means his bond with Toothless could be different, as they are now more alike in a way.
The 'hiccup is part dragon' concept in fanfictions makes the story much more complex and exciting. Hiccup's new nature can introduce new plotlines such as him having to discover his dragon heritage. It can also lead to him having to hide his new abilities from some of the more superstitious vikings in Berk. His physical and mental transformation can create interesting scenarios. For instance, he might have to learn to control his new instincts. And his relationship with the dragons in general could shift, as he is now part of their world in a more direct way than before.