Not remotely offensive. Anita Blake is my pet peeve. I've read others and put them down for the same reason - too much of a badass heroine who isn't particularly vulnerable and acts a little too seasoned, even for an adult - but I gave up a few years ago so my memory isn't great... Urban Shaman was a little better, but still didn't have the emotional resonance of a YA for me. Couldn't get through a Kim Harrison book, but maybe I didn't give it long enough. The first Dresden files was okay but again, just no emotional resonance.
I loved the Sookie Stackhouse books, at least at first, and they were what got me looking for more urban fantasy. I didn't really find other books I liked until I switched to YA. Yes, Sookie was a virgin, and it was kind of stupid. That's not why I liked the first book. I liked that she was a fundamentally introspective character.
It's hard to put my finger on. Not always a lack of emotional depth (although I really, really hate Anita Blake-like characters for that reason) but more of a genre focus on action over introspection, as though only teenagers ever think about the deeper complexities of life or the fate of relationships.
And hey, I'm not an expert on any genre. I'm sure I've missed some good stuff (and some bad stuff). These are just my impressions, strengthened somewhat by me telling friends the kind of book I want to write and them saying "yeah, that should be YA", when I talked about wanting to write something slower paced and more focused on relationships, but not any particular theme of first experiences. But my friends don't know everything, either, so if you've got suggestions in the urban fantasy genre I would be THRILLED to hear about them. Because I really do want to read and write complex adult characters.
Although to go back to the context of firsts, I think when it comes to paranormal elements, that's one of the fun parts of putting it in an adult world. You can be all grown up and still have first experiences, still feel the world rocked around you, lose your footing a little. If the character is already an expert in that world, it's less interesting.
People read for different reasons and look for different things. The characters that turn me off are exactly right for lots of people, and vice versa. So an adult character that's just right for me might seem too angsty to someone else. Such is life.