The story changes a lot. For one, Elena's place in the supernatural world shifts. She goes from being a target of vampires to being one of them. This means she's now part of the 'in - crowd' in a way. Her daily routine would be completely different. Instead of going to school during the day, she'd be prowling at night. And her relationships with the other characters would be redefined. Stefan and Damon would have to see her in a new light, and she might start to have a different understanding of Klaus too, not just as a threat but as someone who has given her a new kind of life.
Caroline, for example, might be more accepting as she is also a vampire. She could help Elena adjust to her new life. Damon, on the other hand, might be jealous or feel threatened that Stefan made Elena a vampire. It could change the power balance between the three of them.
One reason for Elena bashing in fanfiction could be that some fans prefer other characters over her. For example, they might be big fans of Bonnie or Caroline and feel that Elena gets too much attention in the show. So in fanfiction, they might downplay or 'bash' Elena to give more focus to their favorite characters.
Elena's final romantic partner in the Vampire Diaries novel is Damon. Their love story is full of ups and downs, but they overcome all odds to be together.
In such a fanfiction, a lot could unfold. Elena might face conflicts with other supernatural beings or have internal battles with her morality as a vampire. Also, there could be romantic complications with the people in her life.
Katherine turning Elena into a vampire changes her life in many ways. For one, Elena's diet changes. She has to resist the urge to feed on humans. Socially, she becomes an outcast among normal humans. Her perception of the world also changes. She starts to see the vampire society in a different light and has to find her place within it.
It really depends on the perspective. Elena is often seen as the good girl, the one with a pure heart. She represents the moral compass in many fanfictions. But Katherine has this allure of mystery and a long history of survival. If you like characters with depth and a darker side, Katherine might be better in the fanfiction world. However, if you prefer the more traditional heroines, Elena would be the top choice.