A digital thermostat is superior to an analog thermostat because of health and safety, and for monetary reasons. Add to that convenience and accuracy, and you'll see why many homeowners install digital thermostats. Here are 2 advantages to consider:
Over the years, more people have learned about the dangers of mercury in the home. For that reason, many people avoid compact fluorescent light bulbs and other products that include mercury in them. The same goes for thermostats. An analog thermostat needs mercury to work, and there's always the risk of that mercury spilling into your home. A major advantage of using a digital thermostat is that they don't contain any mercury. This is a huge health and safety benefit that trumps any advantage an analog thermostat has.
Saving money on your utilities is important, and a digital thermostat will help you, because you can program your heating and cooling needs ahead of time. For example, choose what temperature you want depending on the time of day, instead of just running your heating-ventilation-air conditioning system all day long at the same temperature. This will make a difference in your electric bill, because your unit won't come on as much.