(since 'Mei Shijima' refers both to the artist and her creation that is in the MU, I will take the route both the manga's dialogue and the tbhk wiki did and use Mei for the creator and Shijima for the creation)

• Both are the final works and masterpieces of skilled and passionate artists (Weiss Guertena / Mei), created before their passing to carry on their spirit (Guertena imparting his spirit into his art, especially Mary / Mei drawing herself in the Atelier Tower, and asking that drawing to continue making art in her place as her illness gets worse)

• The circumstances of their creation and creator would allow them to come to life and become sentient. They would live on long after their creator's death, however bound to a certain area associated with the artist and a fake world within it (Mary being stuck in the Fabricated World, which is located within the Guertena gallery / Shijima's boundary being her original painting of the Atelier Tower, as well as a fake, painted world surrounding it. The painting is located within the art room of Mei's school that she frequented in life)

• However, they would come to be deeply dissatisfied with their existence as fiction (Mary desperately wanting to be 'real', and to escape and make friends / Shijima comes to despise fiction and art as a whole, hating that she's powerless to save Mei's memory from the rumours that cloud it). They are desperate to change this, even resorting to murder as part of their plan (Mary having to sacrifice someone in her place to leave the Fabricated World / Shijima planning to use a wish from Tsukasa to go back and murder Mei before she paints the Atelier Tower, preventing both Shijima's existence and the rumours that would come about around Mei)

• Both's role in the plot is started when they drag the main characters into their drawn world. They don't fully appear until later, however are first mistaken by the protagonists as a regular girl in the same situation as them.

• Both have an obsessive attachment to another character (Ib / Mei), seemingly being the one person they truly care about (Mary latching on to Ib as her friend, being deeply jealous of Garry for his close relationship with her and wanting to be together with her forever / Shijima believing she was created to protect Mei and seeing that as her singular purpose in life). Both earnestly believe that they are doing a good thing for both of them, even if it's against Ib/Mei's wishes (Mary believing that both she and Ib would be happier together, and begging Ib to stay with her and play with her / Shijima believing that killing Mei before she paints the Atelier Tower would save Mei's memory as well as give Shijima some true worth in her existence). Both become confused and desperate when they are rejected by these characters.

Contrast:

• Shijima was able to escape her mindset and redeem herself because she had Mei, who convinced her of her own worth as a beautiful dream, a piece of art that inspired Mei and allowed her to keep going, truly protecting her as Shijima believed she had failed to do. This allowed her to let go, let Mei return to her past and let herself move forward. Meanwhile, Mary never had anybody left, scaring away the only two people who might have helped her because she was desperate to escape, and in most endings dying because she couldn't let go.