Film Camera Gates vs. Digital Sensors
Before HD video was such a common filmmaking tool, there was no real alternative to 35mm and 16mm film. These media capture a relatively large analog image and like all analogs, the larger the sampling area, the better its ability to faithfully reproduce the real world source. In the case of film, a larger sample means more resolution/clarity and less apparent grain. HD is similar to film in that a larger sensor with larger pixels tends to produce cleaner, more resolved images. However due to tremendous advances in codecs and image processing, small sensors can produce exceedingly good images as well.
There are a number of commonly used HD sensor sizes, 1/4", 1/3", 1/2", 2/3". These are all significantly smaller than a frame of 35mm motion picture film but still capture images with very good latitude and color reproduction. With state of the art image processing, a high quality image can be captured with these small chips but there still is a direct correlation between sensor size, quality of optics, and overall aesthetic qualities. The larger the sensor or gate, the more shallow depth of field is created in the image. A large imager combined with a wide lens aperture is the key to creating that sexy depth of field that continues to obsess filmmakers. Another issue directly related to sensor/gate size is the relative Field of View (FoV) that a lens will produce on any given imager. Depending on the size of the sensor, the same optics will produce vastly different images from format to format.
I like to think about HD sensors as if they are the aperture (gate) on a film camera. A lens creates a circular image, it passes through the gate which crops the light to the desired rectangular shape and then the frame is exposed on the film plane. A larger gate exposes a larger frame which results in more captured information. In HD, it's the exact same thing, a larger sensor theoretically captures more picture information and is more faithful to the source.
Take a look at the actual sizes of various film and video formats compared:
Perhaps the real key factor in resolution and image quality though is optics. A lens delivers an image and then it is up to the medium's resolving power to faithfully reproduce it. Bad optics produce a bad image and a good sensor is not going to make it any better. Conversely, superior optics on a comparatively low resolution sensor can look surprisingly good. There's a reason good quality glass such as Cooke S4's and Arri Master Primes costs what they do. You get what you pay for and a plastic piece of junk lens will only disappoint. Because high quality optics are part of the recipe for high quality images, HD cameras with a sensor the size of a Super 35mm frame have been recently developed. Historically the world's finest lens makers; Cooke, Zeiss, Angenieux, etc. have put the most research and money into the development of optics for the 35mm motion picture standard. This is great because the inventory of high quality lenses available at most rental houses can now be used for digital filmmaking.
So far in digital cinematography it seems that good glass on the biggest possible sensor is the best substitute for 35 which continues to be the standard of quality and excellence. It seems like that's really the only goal in the development of digital cinema cameras - to emulate the look of 35mm. I think only when people stop comparing digital to film will signal that digital's potential has been met.