One of the advantages of using a camera with a smaller than APS-C sensor is greater depth of field! One area where this can be helpful is macro photography, were there are times that you simply cannot get enough depth of field without stopping down to crazy apertures like F45 on a full frame camera. At F45 might get you might get the depth of field you want, but it cuts out so much light that photographing anything outside of a controlled environment is out of the question (unless you have portable studio lights and battery packs). One solution used to overcoming this by many amateur, and professional, photographers is focus stacking, which is a process of taking many photos focused at different points, then merging the images in photoshop. Focus stacking is an elegant, yet not always practical, solution.
So how does this come back to using a camera with a smaller imaging sensor? Smaller sensor cameras use super wide angle lenses to give similar focal ranges to what people were familiar with from 35mm film cameras.* The results are twofold, the lenses can be very sharp, even at wide apertures, and the depth of field is so thick that by F4 everything from 1m to infinity is in focus. What does this have to do with macro photography? A lot actually, as I mentioned before, having greater depth of field is an advantage when taking macro photos, because as you get closer to an object the depth of field gets narrower. As a result some compact cameras can offer extremely good macro performance, in the right light.
* The widest 6mm setting on the Nikon P7100 gives a view similar to a 28mm lens on a full frame DSLR