Full Moon wo Sagashite, Kodomo no Omocha (TV) Recommendations
Both shows have comedic elements and fun, but mainly deal with mature and dramatic situations, and mysteries revolving around the female leads.
Since I watched Full Moon wo Sagashite first, I kinda have the same feeling. It's an anime that you would think to be for children, but both have a much deeper storyline hidden in them which makes it really good. I have the feeling that the darker storyline starts sooner in Kodomo no Omocha, but in my opinion they are both worth watching.