I think it should be a flat Proficiency check so all classes have an even playing field.
If it is an illithid power then I think it should use the same ability that the illithids use for their powers.
Not because of my faith in the delicate balance of the 5e system, but because there's something to be said for consistency. You can't have one illithid using Int while another uses Str and a third relies on an acrobatics check.
