Sensors for many dSLRs are smaller than film frames, leading to the infamous crop factor.  Only part of the image formed by a lens designed for a full frame sensor is captured by a sensor that’s smaller than 24mm x 36mm (like most dSLR sensors even today are). The crop factor may be 1.3, 1.5, 1.6, or even 2.0 times. This crop factor can be (seemingly) good for telephoto pictures, but it doesn’t create such a great effect if you really wanted a wide-angle view. A 100mm lens may have the field of view of a 150mm lens, but a 20mm super-wide-angle lens ends up with the viewpoint of a mundane 30mm lens.

Because the image uses only a smaller portion of the lens coverage area, the smaller sensor crops the edges and corners of the image, where aberrations and other defects traditionally hide. You just might be using the best part of your lens if it was originally designed for a film camera.

Of course, vendors are producing lenses designed expressly for smaller sensors, which means that their reduced coverage area must be extraordinarily even in terms of sharpness and light distribution.

But wait, there’s more! Sensors don’t respond to light the same way that film does. Film grains absorb light in roughly the same manner, regardless of its angle of approach to the film surface. A sensor’s photosites, on the other hand, are little pixel-nabbing wells that collect photons best when they drop directly into the bucket, instead of coming in from a steep angle. When you use lenses designed for film on a dSLR, some of the light can hit the side of the well or spill over into adjacent pixels. Unwanted patterns and light fall-off can result, along with flare that happens when photons bounce off the shiny sensor surface, hit the equally shiny rear lens elements, and then reflect back onto the sensor.

Although camera and lens designers have found ways to counter these problems with equipment designed expressly for digital photography, optics created for film cameras might not produce the same uniformly good results. Image quality can vary from lens to lens, based on how well the design meets the needs of digital imaging.

A camera that has an image cropped by the camera’s small sensor gives you more telephoto reach than simply cutting the center out of a full-frame image because of pixel density. A 21 MP crop-factor camera and a 21 MP full-frame camera have the same number of pixels, but the cropped camera packs them all more densely into the area of a smaller sensor. Put a 500mm lens on a 21 MP camera with a 1.5x crop factor, and all 21 megapixels give you the equivalent field-of-view of a 750mm lens on a full-frame camera. When you mount that same lens on a full-frame camera, such as the 21 MP Canon 5 D mark III, cropping out the center portion yields the same field of view, but only 5 megapixels-worth of the full-frame camera’s less dense pixels are used to form the image. The camera with the 1.5x crop factor gives you an image that has more resolution and sharpness. 

Please watch out - Lenses made and meant for smaller format cameras cannot be mounted on full frame cameras where as the lenses meant for full frame can be mounted on any camera body. 

Canon EOS 70 D	Canon EOS 5 D mark III

If you look at the photographs above it quite clear that the image from the larger sensor is the winner. However, if you do not compare the two photographs together and you cant afford a more expensive camera, the small format should not be a problem as such. In comparison ofcourse the full frame shows better colours and depth.