The new Joker is usually rooted in the comic source material. However, there could be variations and additions to add depth or modernize the character for the contemporary audience.
In the 'new 52 joker story', the Joker is up to his usual antics of causing disorder. His actions are often driven by his twisted sense of humor. For example, he sets up elaborate traps for Batman that not only test the Dark Knight's combat skills but also his ability to keep the city from falling into panic. The story also shows his relationship with other villains in the new 52 universe and how he manipulates them to achieve his own ends.
In many ways, it's different. The movie explores the character's psyche in a more in-depth and darker manner than the comics typically do. The setting and events also deviate significantly.
It's somewhat accurate, but there are definitely some creative liberties taken. The movie captures the essence of the character, but the story might deviate in some aspects.
The Joker in the Batman New 52 story evolves in a complex manner. His character is more unhinged than ever. He shows a greater understanding of Batman's weaknesses and uses them to his advantage. For instance, he might target Batman's friends or places that hold sentimental value for Batman. His evolution also includes a more grotesque and disturbing aesthetic. His makeup and overall look seem to be a reflection of his inner state of mind. He is constantly pushing the boundaries of what is considered acceptable behavior, even for a villain in Gotham. His actions have a wider impact on the city, causing not only physical damage but also psychological trauma to the citizens.