Psychopaths/sociopaths (you know, the people who torture and kill for fun) have an inclination to violence. However, Monika herself was trying to avoid being tortured, and she still cared for the other girls and wanted to avoid outright killing/deleting them (source: Dan Salvato's stream), which is why instead of immediately resorting to deletion, she attempted to use less violent techniques like editing their personality, speech, and causing glitches (especially Natsuki/Yuri) in an attempt to drive the other girls away from the player. Further evidence to support that Monika does not have an inclination to violence include the fact that Monika only began altering Sayori's personality after the other girls prevented the player from being able to help Monika with the festival even if the player had picked Monika and that Monika did not alter Natsuki's personality in Act 2. There's also more stuff here.

Sayori also had the benefit of inheriting Monika's knowledge in Act 4. When you start the game without monika.chr and reach the [quick ending],(https://www.youtube.com/watch?v=-2qMzMJBCGw) Sayori says 14 lines and then FUCKING KILLS EVERYONE.

label ch0_kill:
    stop music fadeout 2.0
    scene bg residential_day
    with dissolve_scene_full
    play music t2
    $ s_name = "Sayori"
    show sayori 1b zorder 2 at t11
    s "..."
    s "..."
    s "W-What..."
    s 1g "..."
    s "This..."
    s "What is this...?"
    s "Oh no..."
    s 1u "No..."
    s "This can't be it."
    s "This can't be all there is."
    s 4w "What is this?"
    s "What am I?"
    s "Make it stop!"
    s "PLEASE MAKE IT STOP!"

    $ delete_character("sayori")
    $ delete_character("natsuki")
    $ delete_character("yuri")
    $ delete_character("monika")
    $ renpy.quit()

Many sociopaths also use anxiety and depression as pity plays.

Basically, Sayori displays more traits of sociopathy/psychopathy than Monika, despite many Sayorians saying Monika is a psychopath/sociopath.