I now see AJ Henderson's point in the comments. The argument I made in this posting about the exposure is wrong. While with larger focal length (F) the field of view decreases approximately proportional to 1/F^2, at constant F-number N, the aperture is F/N, which means that the total amount of light per unit time on the sensor is proportional to 1/F^2 * (F/N)^2 = 1/N^2 which does not depend on the F-number.
This means that you have less room to decrease ISO etc. as I sugggested in the original posting, but you still have the advantage of less motion blur and depth of field etc.
Original posting:
Usually moving closer is better (as long you can still focus). By zooming less, you can shoot with longer exposure time without motion blurring due to camera shake. The larger field of view means that you are gathering more light, so this reduces the exposure time you actually need. This then gives you a lot of room to lower the ISO in order to reduce noise. With less noise, a lower noise reduction level is needed. Since noise reduction comes at the expense of resolution, this will also improve the image quality.
Response to comments:
If you zoom more, the field of view as determined by the image on the sensor becomes smaller (sensor size divided by focal length determines the field of view). So, the sensor will get less light. The reduction in the amount of light is approximately quadratic in the focal length. If I reduce the distance to the object by half, then I can approximately reduce the focal length by half so that it still fills the same part of the image. But then I'm going to have 4 times as much light. As far as focussing is concerned, without reducing the F-number, the hyperfocal distance will be approximately reduced by a factor of 4 while I have moved only a factor of 2 closer, so this is a net gain.
So, I would say that from a purely technical point of view where you focus on getting as much information from the subject in your image as clearly as possible, it is usually better to get closer to the subject. From an artistic/esthetic point of view you may well decide that such a picture looks ugly and a picture taken from farther away looks better.