Analog and digital scales have their specific uses. Both types are around the same price, but digital scales are more accurate than analog scales.
Analog scales have round dials, where a pointer moves clockwise according to the weight applied. Markings are equally spaced between the numbers to indicate fractional amounts (1/4, 1/2).
Digital scales have LCD or LED number displays. There are no pointers on a digital scale.
Analog scales can be hard to read depending on the viewing angle. This can pose a problem when the pointer lands between fractional markings.
Digital scales can be programmed to read to 2 or more decimal places. This allows more accuracy than "eyeballing" fractions on analog scales.
Scales are used in delicatessens, grocery stores, product stands, just about anywhere things needs to be weighed. Digital scales are used where precision is needed (pharmacies, labs), when trace amounts (milligrams, coins) are weighed.
The price difference between digital and analog scales is about the same. These prices depend on the quality of the scale--digital scales tend to be more durable.