which is better in a digital camera - optical zoom or digital zoom?

Optical zoom, ignore digital. A mixture of the two is fine but it is still the optical element that provides a quality zoomed image.

What is optical zoom?

Optical zoom lenses physically extend to magnify your subject. A motor controls the lens movement. When you press the switch to "W" or "T," the subject is either magnified or reduced in size. The "W" stands for "wide-angle" (reduce). The "T" stands for "telephoto" (magnify).

What is digital zoom?

Digital zoom crops your image and magnifies the result of the cropping. This magnification process is called interpolation. To make the cropped area bigger, digital zoom makes up, or interpolates, pixels to add to the image, which may give less than satisfactory results. For your purpose, digital zoom is not really zoom, in the strictest definition of the term. What digital zoom does is enlarge a portion of the image, thus 'simulating' optical zoom.

Using the digital zoom allows you to get closer to your subject when you want to be discreet about taking pictures, like at a graduation or a religious ceremony. Sacrificing image quality to capture the moment is more important than not getting the picture at all.

I usually recommend buying a digital camera with at least 3 megapixels resolution because of the better image quality. A 2x optical zoom is disappointing, but not necessarily a show-stopper. A 3x optical zoom is standard with most consumer digital cameras. Some ultra-compact digital cameras may be able to provide only 2x optical zoom. I never bother to check how much digital zoom a camera provides, and ignore the marketing hype surrounding it. I always disable digital zoom in camera, choosing to do my own cropping and enlarging in image editing software.