The cinematic look, partially created by shooting at 24 frames per second looks much smoother and more organic. Many newer camcorders do offer 24 FPS shooting, but they consumer camcorders don't yet offer the sensor and lens capabilities in a larger camera.
Shallow depth of field is seen everywhere in professional cinematography, from blockbuster Hollywood films, to indie films, to current TV commercials. DSLR's paired with f/4 or faster lenses can provide shallow depth of field that looks like something shot for the big screen.
Low light filming that was not possible prior to 2008, continues to get better each year with DSLRs. Full frame sensors are the best option, and can be had for about $2,000 and up if buying a new camera. Sony and Canon have been offering great full frame camera options. However, several other companies compete with them, so in a few years, Nikon or Panasonic may offer something even more appealing.
Color profiles will allow you to shoot your footage flat (less color saturation and lower contrast), allowing you to fine tune the look of your project during editing.
Manual settings set DSLRs apart from prosumer camcorders. Aperture, ISO, Shutter Speed, and Mic recording level can all be controlled in full manual mode.
DSLR cameras with full frame sensors can shoot footage that still looks great at 3200 ISO, something that wasn't possible before 35mm size sensors became affordable and Canon democratized them with the Canon 5D Mark II in late 2008.
See the benefits visually of DSLR Filmmaking in this tutorial.
