Cutout in Flash

I've been using Flash for some time to accomplish animation in a cutout style. In fact, I used Flash as an initial testing ground for the animation I ended up doing under the camera for Production 1 to see if my puppet rigs would work. I also used flash to create several replacement cycles for both the girl and the possum in my film. I find flash real easy to use, and I can animate bitmaps quickly, but in the end, I'm not satisfied with the final look. It's very flat, the options for adding shadows aren't very useful, and their really isn't any options for camera moves, unless you fake it by creating backgrounds that can pan or tilt, or if you scale your whole set incrementally over time.

I made a little cutout piece for our flash class, I would like to see how this same layout could be achieved in a 3D program. I fear that it might be significantly more difficult than working in Flash, but I'm really curious of the options I'd have for manipulating depth, and camera moves/angles.