3 examples
All 3 of these shot handheld with a Nikon D700 and 105mm macro lens:
f/3 ISO 200 1/100
f/11 ISO 1600 1/60
f/32 ISO 6400 1/30
Notice the much shallower depth of field in the first shot at f/3. Basically only the stem is in focus. At f/11 the entire leaf and its reflection is (mostly) in focus but the foreground is still out of focus. By f/32 much more of the foreground and background is in focus, but the aperture is so small that it creates other problems for a handheld shot (slow shutter speed and high ISO which increase both noise and a loss of sharpness due to camera shake). In hindsight I should have taken a shot at f/4 and maybe f/5.6. Would have been interesting to see the tradeoff between depth of field and subject sharpness at those apertures.
I may shoot a series comparing the depth of fields of a DSLR and point-and-shoot (which will actually address the question the OP posed). Point-and-shoots have much smaller sensors than DSLRs, which means that for an equivalent field of view their focal lengths are much, much smaller. Depth of field varies by actual focal length, not by equivalent focal length. So when shooting with a point-and-shoot it's like you are always using an ultra (or even ultra-ultra) wide-angle lens with regards to depth of field. Even at fast apertures, it's often not possible to have a shallow enough depth of field to really isolate a subject with a point-and-shoot. That's one of the reasons why people put up with the added bulk, weight, and cost of DSLRs and fast lenses. On the other hand if your creative intent requires a large depth of field to keep everything in focus, a good point-and-shoot is actually better than a DSLR (assuming you are handholding and don't require the better image quality that a good DSLR/lens combo can offer).