"Moe" is probably not at all the right word to describe it, from what I've heard.
Doing a quick search on it, and it seems to be a Josei genre ("created mostly by women for late teenage and adult female audiences from 15 to 44"), which probably plays a role in why it might have a different feel for you, as genres like that usually revolve around more adult themes and concepts, or so I've heard?
On the flip side of the adult genre would be Seinen, I believe? ("targeted at a 18–30 year old male audience, but the audience can be older with some manga aimed at businessmen well into their 40s"). An example of Seinen manga would be Oyasumi PunPun, which...is supposedly very dark and surrealistic.