They have a similar overarching storyline where 1 person takes the other in as a "pet",
but in kimi wa petto, the "pet" is the one that get's cooked for and pampered, where i'm your pet it's more just like an excuse
I'm your pet is BL, kimi wa petto isn't
They both have it where the one person only feels comfortable and able to be themselves with the "pet"

Both have the theme of some sort of 'Serial Killer Gene' (that in some cases is a 'Genius Gene'), and somewhat explore the ethics using that knowledge

Both are about solving crimes, though Mouse is more about a big overarching case, while Justice in the Dark seems to be broken up into smaller cases that are connected (once it's fully released, this might be different)

Mouse does not have any BL themes, and seems to be more graphic when showing crime scenes