 If you liked
Full Moon wo Sagashite
|
 ...then you might like
Kodomo no Omocha (TV)
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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.