It's more than just the effect it has on the lens. The biggest and probably the most noticeable difference is the effect it has on noise and image quality.
To put it simply, the larger the sensor, the more light it's able to collect. That means a full frame camera doesn't have to amplify the signal as much. That results in a lot less noise.
Image quality is enhanced not only because of the cleaner image, but because the camera doesn't have to perform as much noise reduction on the image. That means an even cleaner and clearer image.
So, yeah there's a lot more to it than just the crop factor.
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James
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