Getting a better picture is mostly dependent upon the person holding the camera.
The more expensive cameras will let you get good pictures in difficult or unusual situations. But it requires that you know something about photography.
When shooting in low light the DSLR has the advantage because of its larger CCD or CMOS sensor assembly.
A larger sensor assembly has larger pixels.
Larger pixels can produce more light for the camera.
The disadvantage is, a larger sensor assembly requires a larger lens, which requires a larger camera.
A larger camera means more weight, which is actually good.
A heavy camera is easier to hold steady.
All DSLR cameras have manual controls so that you can adjust for difficult and special situations.
Only about 5 percent of the non-DSLR cameras have exposure related manual controls.
And even that 5 percent do not have as many manual controls as a DSLR camera.
I have been using cameras both film and digital but I still could not exactly follow how to make a selection of a digital camera with choice of lenses focal distances and how SLR will help getting a better picture